Study of Tank Containers for Foodstuffs

machines

Article Study of Tank Containers for Foodstuffs

Aurelio Liguori 1, Andrea Formato 2,* , Arcangelo Pellegrino 3 and Francesco Villecco 3

1 Degree Course in Transport, University “G. Fortunato”, Viale Raffaele Delcogliano, 12, 82100 Benevento, Italy; [email protected] 2 Department of Agricultural Science, University of Naples “Federico II”, Via Università 100, 80045 Naples, Italy 3 Department of Industrial Engineering, University of Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy; [email protected] (A.P.); [email protected] (F.V.) * Correspondence: [email protected]

Abstract: In this study, we examined a tank container for foodstuff that is generally used for the transport of foodstuffs. With the aid of the “ANSYS R17.0” program code, a numerical model of the tank container for foodstuffs was realized. Further, to validate the considered model, the tank container considered was submitted to the most important ISO tests concerning both its support frame and the tank. The results obtained from the FEM analysis, in terms of displacement for each test, were compared with those provided by the manufacturer and related to the tank container considered, evaluating the difference between the numerical results with the experimental ones. This allowed us to validate the model examined. Furthermore, the results obtained from each test, in terms of stress, have made it possible to locate the areas with the highest equivalent stress and quantify the maximum value, comparing it with the allowable stress. In this way, a better understanding of the structure was achieved, and it was detected that the most stressed area is that of the connections between the container and the frame. Furthermore, modal analysis was carried out, in which the natural frequencies relating to the most dangerous modes of vibrations were found, that is, with the lowest frequency values. Finally, changes for the considered tank container were examined, and it Citation: Liguori, A.; Formato, A.; was found that, by changing parameters, such as the thickness of the plate and skirt, and subsequently Pellegrino, A.; Villecco, F. Study of acting on the arrangement of the corner supports, the highest value of the stresses generated by the Tank Containers for Foodstuffs. loads related to the ISO tests, it is signiﬁcantly lowered, resulting in a better distributed stiffening Machines 2021, 9, 44. https:// of the structure and a reduction, although minimal, of weight. It is evident that this modeling and doi.org/10.3390/machines9020044 validation method, suitably integrated by further calculation modules, can be used in an iterative

Academic Editor: Hamid Reza Karimi optimization process.

Received: 3 January 2021 Keywords: ISO tests; numerical simulation; tank containers for foodstuff Accepted: 18 February 2021 Published: 21 February 2021

Publisher’s Note: MDPI stays neutral 1. Introduction with regard to jurisdictional claims in In the field of freight transport, both by sea and by land, the use of the container is published maps and institutional affil- now a fixed point, thanks to the advantages it involves in terms of costs, efficiency and iations. the capability to support different modes of transport: trains, trucks with trailers and ships [1–3]. The use of containers for the transport of food products has become increasingly widespread. It is interesting to underline that the development of tank containers for foodstuff has imposed the realization of new techniques related to their handling, Copyright: © 2021 by the authors. which, with the possibility of interchanging the means of transport by ship/truck/rail, Licensee MDPI, Basel, Switzerland. constitutes a real science called “interlogistics” [4–6], by virtue of which a revolutionary This article is an open access article transport technique was developed, which has led, among other things, to the possibility distributed under the terms and of directly connecting the production sites of a given asset to the final user of the asset conditions of the Creative Commons considered (door-to-door). All of this is done without performing intermediate handling Attribution (CC BY) license (https:// of the transported goods, with a significant reduction in delivery times and with signif- creativecommons.org/licenses/by/ icant positive implications on the conservation of all the original characteristics of the 4.0/).

Machines 2021, 9, 44. https://doi.org/10.3390/machines9020044 https://www.mdpi.com/journal/machines Machines 2021, 9, 44 2 of 21

transported goods and then of the quality of it [7–9]. In the present study, we studied a tank container for foodstuff, formed by a rectangular steel frame, inside which there was a cylindrical tank used for the transport of fluids or granular materials, very often used in the food agro-industry. The container was designed with particular regard to its frame, analyzed using a FEM model. Subsequently we became interested in the tank container by examining the design of its frame, as the evolution of the project in this field has so far been characterized by a “trial and error” process caused by a lack of traditional methods of analysis. [10–12]. The consequence of this way of designing involved the presence of the following: (a) Excessively robust sections, i.e., oversized; (b) Lack of attention to stiffness issues. In the present research, the conditions were created to fill this gap by showing a method capable of providing design indications capable of leading to less generous but more accurate sizing, making the construction efficient and safer against the danger deriving from an inattentive study of its natural frequencies. The goal was achieved by using the ANSYS program, which made it possible to create a valid FEM model of the tank container. In conclusion, this research basically involved the following steps: 1. State-of-the-art; 2. Creation of the FEM model, based on the indications taken from a real tank container. 3. Simulation of ISO tests and validation of the FEM model. 4. Identification of equivalent high-voltage areas in the chassis. 5. Calculation of natural frequencies and interpretation of results. We then proceeded to stiffen the parts most stressed by carrying out the appropriate reiterations, which led to an improvement of the structure. Therefore, the conditions were created to fill this gap by showing a method capable of providing design indications capable of leading to less generous but more accurate sizing, but more accurate, making the construction efficient and safer against the danger deriving from an inattentive study of its natural frequencies. It was, thus, possible to identify the most stressed parts and appropriately stiffen them, performing the appropriate reiterations that have led to an improvement of the structure [13–15]. In the present work, we tried, as far as possible, to give a schematic and rational organization of both the information collected and the results achieved, in order to provide a linear presentation and facilitate consultation.

2. Tank Container for Foodstuff The basic elements making up a tank container are as follows: - Frame: Placed on both ends of the container, it consists of four corner blocks, two corners upright and two end crosspieces. - Corner blocks: small perforated metal structures, welded on the four lower and upper edges of the tank containers, necessary to allow their gripping, transferring, stacking and anchoring. - End crosspiece: transverse structural element of the lower (upper) part of the frame, of which it connects the lower (upper) corner blocks. - Side spars: a longitudinal structural element that connects the lower corner blocks of the two end frames. - Corner upright: a vertical structural element that connects two corner blocks on both sides of an end frame, one upper and the other lower, and thus forming a corner structure. - Tank. The corner blocks are suitable for housing the “twistlocks” (rotating pins), which allow us to handle the tank containers or to ﬁx them together (as happens in stacking); in Machines 2021, 9, 44 3 of 21

fact, by rotating their lever, they act as a more stable connection between the tank container and the structure on which they have to be located [16,17]. Tank containers must comply with ISO standards, in order to enjoy the benefits of the existence of modern and global infrastructure, increasingly available to handle ISO containers [18,19]. The ISO tank container is a large container for fluids or powders, and it has considerable flexibility; in fact, its transport can take place by road, rail or ship, with the possibility of combining the three ways, with advantages in terms of costs and transport safety. It consists of a single cylindrical tank, called “tank body”, arranged inside a rectangular steel frame; furthermore, the whole structure is in accordance with ISO standards, in particular ISO 1496/3 [20,21]. The most common dimensions are a length of 6.058 m, a height of 2.591 m and standard width of 2.438 m. Furthermore, the tare generally varies between 3000 and 5000 kg; by tare, we mean the mass of the empty tank container in its normal operating conditions, i.e., including all accessories and associated equipment. Today, tank containers can carry a wide range of very different products, such as liquid food products, such as wine, fruit juices, oil, starch, milk, sugar, etc. The most requested accessories for tank containers are inherent to the thermoregulation of the transported product [22–25]. Furthermore, we must keep in mind that the tank container market is and will be a niche market compared to the box container market, but not negligible. In fact, we must take into account that a tank container has a purchase price that often exceeds that of a box container by ten times, and many transport companies are investing in tank containers, rather than in new tankers, because they are driven by the advantages due to the great versatility related to its transport by road, ship and train [26]. Addressed in this way, a study was performed, to improve the design of tank containers by mean numerical modeling [27].

3. Materials and Methods The 3D model of the tank container was realized by mean the “Solid Works” program, and it was subsequently imported, as an IGES ﬁle, into the “ANSYS R17” program code to perform the numerical simulations. Only one-eighth of the model was designed and then reﬂected to generate the entire model, on which we reported the few asymmetries geometric. To model the considered geometry, we used the “beam4” elements for the frame and the “shell63” elements for the tank, the octagonal plate, and the skirt; by doing so, it was possible to “mesh” the whole model by reducing the total number of elements used [28–30]. The model, shown in Figure1, was examined, considering it substantially made up of four basic elements: 1. A cylindrical tank, 2. Two skirts, Machines 2021, 9, x FOR PEER REVIEW 4 of 21 3. Two octagonal end plates, 4. The frame.

Figure 1. Model of the tank container. Figure 1. Model of the tank container. Once the geometric model was realized, the “mesh” was performed. The generation of theOnce mesh the geometric was realized model according was realized, to the th “freee “mesh” meshing” was method,performed. but The it wasgeneration suitably of the mesh was realized according to the “free meshing” method, but it was suitably thickened in the connection area between frame and tank where more precise results are desired (Figure 2).

Figure 2. Mesh of the considered model.

After to have realized the geometric model, the numerical simulations of the experimental tests ISO for tank container, were performed, defining the constraints and the loads and obtaining the output values of the following: - Nodal displacements and rotations; - Normal and bending stresses along y and z; - Normal stress and flexion deformations along y and z; - Equivalent stresses according to Von Mises; - Maximum and minimum normal stresses calculated by default by ANSYS.

4. Experimental Tests ISO for Tank Container The regulations governing the transport of goods require that before the mass production of a tank container, a manufacturer have to realize a prototype and, to demonstrate its suitability, submitting it to various tests, static and dynamic, in special laboratories, approved and recognized by the competent authorities of different nations. There- fore, the structural tests for the tank containers are as follows: - Storage test; - Lifting test using the upper or lower corner blocks; - Pressure test; - Test with air; - Test with water; - Longitudinal or transverse stiffness test;

Machines 2021, 9, x FOR PEER REVIEW 4 of 21

Figure 1. Model of the tank container. Machines 2021, 9, 44 4 of 21 Once the geometric model was realized, the “mesh” was performed. The generation of the mesh was realized according to the “free meshing” method, but it was suitably thickened in the connection area between frameframe and tank where more precise results are desired (Figure2 2).).

Figure 2. Mesh of the considered model.

After to have realized the geometric model, the numerical simulations of the experi- After to have realized the geometric model, the numerical simulations of the experimental tests ISO for tank container, were performed, deﬁning the constraints and the loads mental tests ISO for tank container, were performed, defining the constraints and the and obtaining the output values of the following: loads and obtaining the output values of the following: - Nodal displacements and rotations; - Nodal displacements and rotations; - Normal and bending stresses along y and z;

-- Normal and stress bending and ﬂexion stresses deformations along y and along z; y and z;

-- NormalEquivalent stress stresses and flexion according deformations to Von Mises; along y and z;

-- EquivalentMaximum andstresses minimum according normal to Von stresses Mises; calculated by default by ANSYS. - Maximum and minimum normal stresses calculated by default by ANSYS. 4. Experimental Tests ISO for Tank Container 4. Experimental Tests ISO for Tank Container The regulations governing the transport of goods require that before the mass production ofThe a tankregulations container, governing a manufacturer the transport have of to realizegoods require a prototype that before and, to the demonstrate mass pro- ductionits suitability, of a tank submitting container, it toa manufacturer various tests, have static to and realize dynamic, a prototype in special and, laboratories, to demon- strateapproved its suitability, and recognized submitting by the it competent to various authoritiestests, static of and different dynamic, nations. in special Therefore, laborato- the ries,structural approved tests forand the recognized tank containers by the arecompet as follows:ent authorities of different nations. There- fore,- Storagethe structural test; tests for the tank containers are as follows: -- StorageLifting testtest; using the upper or lower corner blocks; -- LiftingPressure test test; using the upper or lower corner blocks; -- PressureTest with test; air; -- Test with water;air; -- TestLongitudinal with water; or transverse stiffness test; -- LongitudinalInspection of or all transverse welds. stiffness test; At pre-set time intervals, we performed the tests, depending on the type of tank and its relative operating time, to ensure its maximum safety. For example, the air test, repeated every two and a half years, makes it possible to check whether the tank is still hermetically sealed. However, the best operators in the industry carry out these tests more often, to increase the safety.

5. Test ISO Description For the considered tank container, we carried out the following tests, which were performed by the CAIB agency (Companie Auxilliere Industrie Belgique), and the methods of realization are shown in detail in “ISO 1496-3: 1995 (E), section 6.2–6.13” (Table1)[ 31,32]. Machines 2021, 9, 44 5 of 21

Table 1. ISO standard test on tank container.

N◦ Test 1 Stacking 2 Lifting for upper corner blocks 3 Lifting for lower corner blocks 4 Transverse stiffness 5 Longitudinal stiffness 6 Restraint

Described below are the tests considered in Table1: (1) Stacking test: It has aimed to verify the stacking capacity of a tank container, that is, its ability to support a determined number of them at full load, of the same nominal size and maximum gross mass, in the worst conditions, that for stacking correspond to those of transport by ship. In reality, tank containers almost never have the same weight, so the stacking always takes place in such a way that the lighter one is located in a higher position. However, in order to take into account the accelerations due to the worst wind and sea conditions, a multiplicative coefﬁcient of 1.8 is adopted, in accordance with studies and measurements carried out in this regard in 1980 (BEAU fort 11). Referring, according to the standards, to ﬁve tank containers superimposed on a sixth, the total load Q on the latter is 3,178,440 N, obtained by the following formula:

Q = 1.8 · R · n · g (1)

where “R” is the maximum gross mass, equal to 36,000 kg, “n” is the number of superimposed containers equal to 5 and “g” is the acceleration of gravity. The four uprights, through the corner blocks, must each support a vertical load of about 800,000 N, not exactly centroidal, but with eccentricity (lateral of 25.4 mm and longitudinal of 38 mm) born from the sum of the clearance existing between the containers and with the guide cells on the ship. We placed the tank container, full of water, on a special installation that was blocked by the lower corner blocks; then we performed the test by applying the aforementioned loads on the four uprights. The test carried out according to the indications of ISO 1496/3 resulted in the displacements along X, Y and Z, in mm, of the four vertical uprights, measured at the highest point of contact between the uprights and the octagonal plates and reported in Table2.

Table 2. Stacking test results.

Displacement along Displacement along Displacement along Upright x(mm) y(mm) z(mm) A 0.65 2.00 0.27 B 0.7 2.26 0.52 C 0.6 2.18 0.45 D 0.7 2.16 0.43 mean 0.66 2.15 0.42

Lifting test: It has aimed to check the tank container’s ability to strengthen to the stresses due to the forces of inertia resulting from the acceleration of the payload upon its vertical lifting, under full load conditions. Realized through its upper or lower ISO corner blocks, carried out by a crane equipped with locks such as to avoid, during the lifting operation, the twisting of the container, the base of which, however, is free to bend. The tank is water ﬁlled, and an additional load of 400,000 N is applied to it, with the use of four Machines 2021, 9, 44 6 of 21

belts connected to hydraulic pistons. Finally, the tank container, is suspended for a period of 5 min, under these load conditions. Deformations measurements of the tank and frame in the lifting direction are usually made. (2) Lifting from the upper corner blocks: the measurements are taken for this test both in the midpoint of the lower part of the tank and in the midpoint of the two longitudinal spars. In Table3, the results are shown.

Table 3. Displacements detected during the lifting from the upper corner blocks.

Element Displacements (mm) tank 2.0 spar 1.8

(3) Lifting from the lower corner blocks: The measurements for this test are taken both at the midpoint of the lower part of the tank and at the midpoint of the two longitudinal spars. In Table4, the results are shown.

Table 4. Displacements detected during the lifting from the lower corner blocks.

Element Displacements (mm) tank 1.6 spar 1.5

(4) Transverse stiffness test: It has aimed to verify the tank container’s ability to strengthen the stresses due to transverse forces caused by the ship’s rolling motion. Ac- cording to the standards, the frame is constrained by the four lower corner blocks and it is applied a force of 150,000 N transversely to each upper corner block. The average value found at the end of the test is 3 mm, measured at the highest point of contact between the uprights and the octagonal plates. (5) Longitudinal stiffness test: It has aimed to verify the tank container’s ability to strengthen the stresses due to longitudinal forces due to the ship’s 15◦ pitch and a period of 8 s. According to the standards, it is applied a force of 75,000 N longitudinally to each upper corner block of the frame, binding the base through the corner blocks. The average value found at the end of the test is 15 mm, measured at the highest point of contact between the uprights and the octagonal plates. (6) Restraint test: It has aimed to exam the “locking aptitude”. The test is performed to evaluate the ability of a fully loaded tank container, during transport on rails, to strength to the forces of inertia due to a deceleration of 2 g, when only the base of its frame, is locked by the corner blocks and the lower crosspieces. The tank is water ﬁlled, and the maximum gross mass R is 36,000 kg; therefore, the force involved is equal to 2·g·R, that is, 706,000 N applied uniformly on the contact areas between the tank and the frame by special equipment. The deformation value found at the end of the test is 4 mm, measured at the highest point of contact between the uprights and the octagonal plates. The overall dimensions of the ISO tank container considered, on which the CAIB has performed the tests, are 2438 m × 2591 m × 6058 m. The frame beams have a box-like section, except in a small section (about 30 cm) of the lower end crosspiece next to the loading and unloading valve, in which the section is solid with dimensions of 150 × 40 mm2. In particular, only in the uprights, the sections are square, while in the other beams, they are rectangular; in Table5, we summarize the geometric characteristics of the sections. Machines 2021, 9, 44 7 of 21

Table 5. Geometric and inertial characteristics.

Moment of Moment of Dimension Thickness Mass Section Inertia Inertia of Torsion mm mm Kg/m cm2 cm4 cm4 uprights 150 × 150 20 70.2 98.0 2795 4726 Ixx = 2320 spar 180 × 100 12 47.0 59.9 2130 Iyy = 886 Supports Ixx = 908 140 × 80 10 30.6 38.9 862 Corner Iyy = 362

The material used for the beams is “EN10210/S355 J2H”, steel equivalent to “FE510D” steel, and it has the following mechanical characteristics: - E = 20,600 daN/mm2 Young module 2 - σs = 35.5 daN/mm Yield stress 2 - σr = 52.0 daN/mm Breakdown stress -G = 78,400 daN/mm2 Tangential modulus of elasticity The tank is the maximum gross mass, equal to 36, of 8 mm on the shell and 10 mm on the bottom, and with 316 L steel is formed, having the following mechanical characteristics: - E = 19,300 daN/mm2 Young module 2 - σs = 24.0 daN/mm Yield stress The two octagonal end plates have a central hole with a diameter of 2 m and a thickness of 20 mm. At the end frame and to the skirt are welded, which in turn has an internal diameter of just over 2 m (that is, with the space required to perform the welding with the plate) and a thickness of 45 mm; both are made of “EN10210/S355” steel. The tare weight MachinesMachines 20212021,, 99,, xx FORFOR PEERPEER REVIEWREVIEW 88 ofof 2121 of the tank container is about 4600 kg, and the dimensions of the different elements that form the tank container are reported in Figures3–5.

FigureFigureFigure 3.3. SideSide 3. Side view.view. view.

FigureFigureFigure 4.4. UpperUpper 4. Upper view.view. view.

FigureFigure 5.5. FrontFront view.view.

RealizedRealized thethe FEMFEM modelmodel ofof thethe tanktank contcontainerainer andand knowingknowing thethe modemode ofof applicationapplication ofof thethe loadsloads accordingaccording toto “ISO“ISO 1496-3:1496-3: 19951995 (E),(E), sectionsection 6.2–6.13”,6.2–6.13”, eacheach ofof thethe teststests de-de- scribedscribed aboveabove waswas simulated,simulated, andand thethe resultsresults werewere comparedcompared withwith thethe realreal valuesvalues availa-available,ble, kindlykindly providedprovided byby CAIB.CAIB. Further,Further, wewe usedused aa safetysafety coefficientcoefficient ofof 1.51.5 forfor thethe stresses.stresses. ItIt gavegave usus thethe allowableallowable stressstress ofof thethe twotwo steelsteelss used,used, forfor thethe valuesvalues indicatedindicated inin TableTable 6.6.

TableTable 6.6. YieldYield andand allowableallowable stressstress ofof thethe twotwo typestypes ofof steelsteel used.used.

ElementElement Material Material Yield Yield StressStress Allowable Allowable StressStress TankTank 316L316L steelsteel 0.2400.240 ∙ ∙ 10 10⁄⁄ 0.1600.160 ∙ ∙ 10 10⁄⁄ FrameFrame Fe510DFe510D steelsteel 0.3550.355 ∙ ∙ 10 10⁄⁄ 0.2400.240 ∙ ∙ 10 10⁄⁄

ForFor thethe determinationdetermination ofof thethe displacementsdisplacements andand thethe stressstress state,state, forfor thethe consideredconsidered model,model, thethe followingfollowing assumptionsassumptions werewere made:made: 1.1. PurelyPurely elasticelastic deformationsdeformations andand absenceabsence ofof breaks;breaks; 2.2. PerfectlyPerfectly isotropicisotropic andand homogeneoushomogeneous materials;materials; 3.3. LengthLength ofof thethe elements,elements, suchsuch asas toto ensureensure thatthat thethe edgeedge effectseffects areare negligible;negligible; 4.4. NoNo thermalthermal expansion.expansion.

Machines 2021, 9, x FOR PEER REVIEW 8 of 21

Figure 3. Side view.

Machines 2021, 9, 44 8 of 21

Figure 4. Upper view.

FigureFigure 5. 5. FrontFront view. view.

RealizedRealized the the FEM FEM model model of of the the tank tank cont containerainer and and knowing knowing the the mode mode of of application application ofof the loads accordingaccording to to “ISO “ISO 1496-3: 1496-3: 1995 1995 (E), (E), section section 6.2–6.13”, 6.2–6.13”, each each of the of tests the describedtests de- above was simulated, and the results were compared with the real values available, kindly scribed above was simulated, and the results were compared with the real values availa- provided by CAIB. Further, we used a safety coefﬁcient of 1.5 for the stresses. It gave us ble, kindly provided by CAIB. Further, we used a safety coefficient of 1.5 for the stresses. the allowable stress of the two steels used, for the values indicated in Table6. It gave us the allowable stress of the two steels used, for the values indicated in Table 6. Table 6. Yield and allowable stress of the two types of steel used. Table 6. Yield and allowable stress of the two types of steel used. Element Material Yield Stress Allowable Stress Element Material Yield Stress Allowable Stress · 9 2 · 9 2 TankTank 316L 316L steel steel 0.2400.240 ∙10 N/m⁄ 0.1600.160 ∙10 N/m⁄ 9 2 9 2 FrameFrame Fe510D Fe510D steel steel 0.3550.355 ∙·10 N/m⁄ 0.2400.240 ∙·10 N/m⁄

ForFor the the determination determination of of the the displacements displacements and and the the stress stress state, state, for for the the considered model,model, the the following following assumptions assumptions were were made: made: 1.1. PurelyPurely elastic elastic deformations deformations and and absence absence of of breaks; breaks; 2.2. PerfectlyPerfectly isotropic isotropic and and homogeneous homogeneous materials; materials; 3.3. LengthLength of of the the elements, elements, such such as as to to ensure ensure that that the the edge edge effects effects are are negligible; negligible; 4.4. NoNo thermal thermal expansion. expansion. On the meshed model, ﬁrst interlocking constraints on the base of the frame were applied, and then subsequently the loads on the four uprights, making sure to also consider the eccentricity. This was done with the aid of four small appendices, connected to the ends of the uprights and suitably arranged, on which the decentered load of the required value was applied. Furthermore, a veriﬁcation on the combined bending and compressive stress was performed, and for that, the critical load for the uprights was determined to be equal to 0.427·109 N. Considering the load due to stacking, we performed a numerical simulation, and the following results were obtained: 1. Displacements along Y-axis An average value of displacement along Y equal to about 2 mm was calculated (Figure6 ). This value, compared with that of 2.15 mm, provided by the manufacturer, gives us a percentage error of about 7%. Machines 2021, 9, x FOR PEER REVIEW 9 of 21

Machines 2021, 9, x FOR PEER REVIEW 9 of 21

On the meshed model, first interlocking constraints on the base of the frame were applied,On theand meshed then subsequently model, first the interlocking loads on the co nstraintsfour uprights, on the making base of sure the toframe also werecon- siderapplied, the andeccentricity. then subsequently This was done the loads with onthe the aid four of four uprights, small appendices,making sure connected to also con- to thesider ends the ofeccentricity. the uprights This and was suitably done with arrang theed, aid on of which four small the decentered appendices, load connected of the re- to quiredthe ends value of the was uprights applied. and Furthermore, suitably arrang a verificationed, on which on the the combined decentered bending load andof the com- re- pressivequired value stress was was applied. performed, Furthermore, and for that,a verification the critical on loadthe combined for the uprights bending was and deter- com- minedpressive to stress be equal was to performed, 0.427∙109 N and. Considering for that, the the critical load dueload to for stacking, the uprights we performed was deter- a minednumerical to be simulation, equal to 0.427 and ∙the109 followingN. Considering results the were load obtained: due to stacking, we performed a numerical1. Displacements simulation, alongand the Y-axis following results were obtained: 1.An Displacements average value along of displacement Y-axis along Y equal to about 2 mm was calculated (Fig- ure 6).An This average value, value compared of displacement with that ofalong 2.15 Y mm, equal provided to about by 2 mmthe manufacturer,was calculated gives(Fig- Machines 2021, 9, 44 9 of 21 ureus a 6). percentage This value, error compared of about with 7%. that of 2.15 mm, provided by the manufacturer, gives us a percentage error of about 7%.

Figure 6. Displacements along y. FigureFigure 6. DisplacementsDisplacements along along y. y. 2. Displacements along X-axis 2. Displacements along X-axis 2.An Displacements average value along of displacement X-axis along X equal to 0.58 mm was calculated (Figure An average value of displacement along X equal to 0.58 mm was calculated (Figure7), An average value of displacement along X equal to 0.58 mm was calculated (Figure 7),which which compared compared with with that that of 0.66 of 0.66 mm, mm, provided provided by the by manufacturer, the manufacturer, gives usgives a percentage us a per- centage7),error which of error about compared of 12%. about with 12%. that of 0.66 mm, provided by the manufacturer, gives us a percentage error of about 12%.

FigureFigure 7. DisplacementsDisplacements along along x. x. Figure3. 7. Displacements Displacements along along x.Z -axis An average value of displacement along Z equal to 0.18 mm was calculated (Figure8 ), which, compared with the value of 0.42 mm, provided by the manufacturer, gives a percentage error of about 57%, which is much higher than the previous ones and could be attributed to a lack of the adopted FEM model. In general, it is interesting to observe how there are different values in the two end frames; in fact, they differ by an order of magnitude, and this is due to the presence of the discontinuity in one of the two plates, due to the need for space for the use of the loading and unloading valve. Machines 2021, 9, x FOR PEER REVIEW 10 of 21 Machines 2021, 9, x FOR PEER REVIEW 10 of 21

3. Displacements along Z-axis 3.An Displacements average value along of displacement Z-axis along Z equal to 0.18 mm was calculated (Figure 8), which,An average compared value with of displacement the value of along0.42 mm, Z equal provided to 0.18 by mm the was manufacturer, calculated (Figuregives a 8),percentage which, compared error of about with 57%, the value which of is 0.42much mm, higher provided than the by previous the manufacturer, ones and could gives be a percentageattributed to error a lack of aboutof the 57%,adopted which FEM is muchmodel. higher In general, than the it is previous interesting ones to andobserve could how be attributedthere are different to a lack valuesof the adoptedin the two FEM end model. frames In; in general, fact, they it is differ interesting by an orderto observe of magni- how there are different values in the two end frames; in fact, they differ by an order of magni- Machines 2021, 9, 44 tude, and this is due to the presence of the discontinuity in one of the two plates, due10 of to 21 tude,the need and for this space is due for to the the use pr esenceof the loading of the discontinuity and unloading in valve.one of the two plates, due to the need for space for the use of the loading and unloading valve.

Figure 8. Displacement along z. FigureFigure 8. 8. DisplacementDisplacement along along z. z. VerificationVeriﬁcation ofof thethe stresses stresses generated generated on on the the whole whole structure structure was was performed, performed, the resultsthe re- Verification of the stresses generated on the whole structure was performed, the re- sultsof which of which are highlighted are highlighted in Figure in Figure9, and 9, it wasand seenit was that seen the that maximum the maximum equivalent equivalent stress, sultsstress,for both of for which materials both are materials highlighted used, does used, not indoes exceedFigure not exceed9, the and admissible itthe was admissible seen one, that so one, thatthe so themaximum that structure the structureequivalent is able tois stress,ablestrength to for strength to both the materials load to the applied load used, applied within does the notwithin safety exceed the margins safetythe admissible margins imposed. one,imposed. Furthermore, so that Furthermore, the westructure detected we is abledetectedthe maximumto strength the maximum value to the of load thevalue applied equivalent of the within equivalent stress the in safety thestress contact margins in the area contact imposed. between area Furthermore, between the upright theand up-we detectedrightthe octagonal and the the maximum octagonal end plate. valueend plate. of the equivalent stress in the contact area between the upright and the octagonal end plate.

Figure 9. Plot of the maximum equivalent stress for the considered structure. Figure 9. Plot of the maximum equivalent stress for the considered structure. 6. Lifting by Upper-Corner Blocks 6. Lifting by Upper-Corner Blocks The tank container was constrained by its four upper-cornerupper-corner blocks, making the structure isostatic, but also allowing it to deform, under the applied load, just as would structureThe tankisostatic, container but also was allowing constrained it to deform,by its four under upper-corner the applied blocks, load, just making as would the happen in the case of a lift of this type. As regards the loads, we simulated the presence structurehappen in isostatic, the case but of aalso lift ofallowing this type. it to As deform, regards under the loads, the applied we simulated load, just the as presence would happenof water in by the considering case of a lift the of pressure this type. that As thisregards applies the onloads, the we lower simulated half of thethe tank,presence and then using a macro created by us in ANSYS code, the pressure on each element was calculated, putting it in relation to the position it occupies inside the tank. To make this, it was necessary to change the type of mesh on the shell, using shell elements 63, with a more regular shape, to have better distribute the pressure inside it. The additional load of 400,000 N applied by belts on the shell of the tank was considered by increasing the weight and by acting on the density; ﬁnally, an acceleration of 2 g upwards was applied to the whole structure. It can be seen, by examining the displacements and the deformation, how the tank deforms, to expand in its underlying part and to contract in the lateral one. The displacement of the spars in their midpoint is equal to 1.8 mm (Figure 10), which coincides Machines 2021, 9, x FOR PEER REVIEW 11 of 21 Machines 2021, 9, x FOR PEER REVIEW 11 of 21

of water by considering the pressure that this applies on the lower half of the tank, and of water by considering the pressure that this applies on the lower half of the tank, and then using a macro created by us in ANSYS code, the pressure on each element was cal- then using a macro created by us in ANSYS code, the pressure on each element was calculated, putting it in relation to the position it occupies inside the tank. To make this, it culated, putting it in relation to the position it occupies inside the tank. To make this, it was necessary to change the type of mesh on the shell, using shell elements 63, with a was necessary to change the type of mesh on the shell, using shell elements 63, with a more regular shape, to have better distribute the pressure inside it. The additional load of more regular shape, to have better distribute the pressure inside it. The additional load of 400,000 N applied by belts on the shell of the tank was considered by increasing the weight 400,000 N applied by belts on the shell of the tank was considered by increasing the weight and by acting on the density; finally, an acceleration of 2 g upwards was applied to the and by acting on the density; finally, an acceleration of 2 g upwards was applied to the whole structure. It can be seen, by examining the displacements and the deformation, how Machines 2021, 9, 44 whole structure. It can be seen, by examining the displacements and the deformation,11 how of 21 the tank deforms, to expand in its underlying part and to contract in the lateral one. The the tank deforms, to expand in its underlying part and to contract in the lateral one. The displacement of the spars in their midpoint is equal to 1.8 mm (Figure 10), which coincides displacement of the spars in their midpoint is equal to 1.8 mm (Figure 10), which coincides with the real value; but on the other hand, there is a lowering of the tank at its midpoint withwith thethe realreal value;value; butbut onon thethe otherother hand,hand, therethere isis aa loweringlowering ofof thethe tanktank atat itsits midpointmidpoint equal to about 1 mm, which gives an error of 50% in default compared to the real one. equalequal toto aboutabout 11 mm,mm, whichwhich givesgives anan errorerror ofof 50%50% inin defaultdefault comparedcompared toto thethe realreal one.one.

Figure 10. Nodal displacements. FigureFigure 10.10. Nodal displacements. The equivalent stresses calculated according to Von Mises are below the allowable The equivalentequivalent stresses calculated accordingaccording to Von MisesMises areare belowbelow thethe allowableallowable ones (Figure 11), and the maximum value detected is 0.575 ∙ 1088 N/m22 near the connection onesones (Figure(Figure 1111),), andand thethe maximummaximum value value detected detected is is 0.575 0.575· 10∙ 108N/m N/m2 near the connection of the tank with the skirts. As regards the frame beams, the normal and bending stress ofof thethe tanktank withwith thethe skirts.skirts. AsAs regardsregards thethe frameframe beams,beams, thethe normalnormal andand bendingbending stressstress tension,tension, which, which, in in ANSYS, ANSYS, are are indicated indicated as as “N “Nmis1”,mis1”, have have detected detected that that the the most most stressed stressed tension, which, in ANSYS, are indicated as “Nmis1”, have detected that the most stressed areaarea is is that that part part of of the the lower lower crosspiece crosspiece in in which which the the section section is is reduced, reduced, due due to to the the presence presence area is that part of the lower crosspiece in which the section is reduced, due to the presence ofof the the loading loading and and unloading unloading valve. valve. of the loading and unloading valve.

FigureFigure 11. 11. TheThe equivalent equivalent stresses stresses calculated calculated according according to to Von Von Mises. Figure 11. The equivalent stresses calculated according to Von Mises. 7. Lifting through Lower Corner Blocks The load application method is the same as in the previous case, but the lifting grip changes, so the constraints have to be located to the lower corner blocks. The deformed has the same shape as that due to the lifting for the upper corner blocks, but with lower values. The displacement of the spars in their midpoint is equal to 1.6 mm (Figure 12), which with respect to the real value of 1.5 mm, gives an error of 6.5%. Then, the lowering of the tank was determined in its midpoint equal to 0.8 mm, which gives, as in the previous case, an error of 50% below the real one of 1.6 mm. The equivalent stresses calculated according to Von Mises are below the allowable ones (Figure 13), and the maximum value detected is 0.551 ·108 N/m2, near the connection of the tank with the skirts. MachinesMachines 20212021,, 99,, xx FORFOR PEERPEER REVIEWREVIEW 1212 ofof 2121

7.7. LiftingLifting throughthrough LowerLower CornerCorner BlocksBlocks TheThe loadload applicationapplication methodmethod isis thethe samesame asas inin thethe previousprevious case,case, butbut thethe liftinglifting gripgrip changes,changes, soso thethe constraintsconstraints havehave toto bebe locatedlocated toto thethe lowerlower cornercorner blocks.blocks. TheThe deformeddeformed hashas thethe samesame shapeshape asas thatthat duedue toto thethe liftinliftingg forfor thethe upperupper cornercorner blocks,blocks, butbut withwith lowerlower values.values. TheThe displacementdisplacement ofof thethe sparsspars inin ththeireir midpointmidpoint isis equalequal toto 1.61.6 mmmm (Figure(Figure 12),12), whichwhich withwith respectrespect toto thethe realreal valuevalue ofof 1.51.5 mm,mm, givesgives anan errorerror ofof 6.5%.6.5%. Then,Then, thethe loweringlowering ofof thethe tanktank waswas determineddetermined inin itsits midpointmidpoint equalequal toto 0.80.8 mm,mm, whichwhich gives,gives, asas inin thethe previ-previ- ousous case,case, anan errorerror ofof 50%50% belowbelow thethe realreal oneone ofof 1.61.6 mm.mm. TheThe equivalentequivalent stressesstresses calculatedcalculated Machines 2021, 9, 44 12 of 21 accordingaccording toto VonVon MisesMises areare belowbelow thethe allowableallowable onesones (Figure(Figure 13),13), andand thethe maximummaximum valuevalue detecteddetected isis 0.5510.551 ∙∙101088 N/mN/m22,, nearnear thethe connectionconnection ofof thethe tanktank withwith thethe skirts.skirts.

FigureFigure 12. 12. NodalNodal displacement.displacement.

Figure 13. Equivalent stress. FigureFigure 13.13. EquivalentEquivalent stress.stress. The normal stress and bending stress of the frame beams indicate that the most The normal stress and bending stress of the frame beams indicate that the most stressedThe areanormal is, once stress again, and that bending part of stress the lower of the crossbar, frame beams where theindicate section that is reduced.the most stressedstressed areaarea is,is, onceonce again,again, thatthat partpart ofof ththee lowerlower crossbar,crossbar, wherewhere thethe sectionsection isis reduced.reduced. 8. Transverse Stiffness 8. Transverse Stiffness 8. TransverseConstrained Stiffness the tank container by the lower corner blocks, a load of 150,000 N was appliedConstrainedConstrained to each of thethe the tanktank four containercontainer upper corner byby thethe blocks lowelowerr in cornercorner the cross blocks,blocks, direction. aa loadload of Theof 150,000150,000 deformation NN waswas appliedappliedshows how toto eacheach the modelofof thethe four deformsfour upperupper differently cornercorner blocksblocks in the inin two thethe frames, crosscross direction.direction. the deformation TheThe deformationdeformation is greater showswhereshows therehowhow the isthe the modelmodel discontinuity deformsdeforms ofdifferentlydifferently the octagonal inin thethe plate. twotwo Theframes,frames, nodal thethe displacements deformationdeformation is identiﬁedis greatergreater in the highest point of contact between the frame and the upright, have an average value of 2.4 mm, which, compared with the real one of 3 mm, gives an error of 20% (Figure 14).

Machines 2021, 9, x FOR PEER REVIEW 13 of 21 Machines 2021, 9, x FOR PEER REVIEW 13 of 21

where there is the discontinuity of the octagonal plate. The nodal displacements identified where there is the discontinuity of the octagonal plate. The nodal displacements identified Machines 2021, 9, 44 in the highest point of contact between the frame and the upright, have an average13 value of 21 inof the2.4 mm,highest which, point compared of contact with between the real the one frame of 3and mm, the gives upright, an error have of an 20% average (Figure value 14). of 2.4 mm, which, compared with the real one of 3 mm, gives an error of 20% (Figure 14).

Figure 14. Nodal displacements. Figure 14. Nodal displacements.

It was noted, considering the equivalent stresses according to Von Von Mises (Figure 1515),), It was noted, considering the equivalent stresses according to Von Mises (Figure 15), that the maximummaximum reachedreached isis equalequal toto 0.1480.148· ∙10 1099 N/mN/m22 inin the the area area between between skirt skirt and and tank, that the maximum reached is equal to 0.148 ∙ 109 N/m2 in the area between skirt and tank, which does not exceed the allowable stress. In addition, we detected high stress valuesvalues inin which does not exceed the allowable stress. In addition, we detected high stress values in the contact areas betweenbetween thethe plateplate andand thethe lower-endlower-end crosspiece.crosspiece. the contact areas between the plate and the lower-end crosspiece.

Figure 15. Equivalent stress. Figure 15. Equivalent stress. The normal stress stress and and bending bending stress stress of of th thee frame frame beams beams take take values values below below the theal- allowablelowableThe one,normal one, and and stressthe the most mostand stressed stressedbending point pointstress is is ofthe the th one onee frame next next tobeams to the the lower lowertake valuesright corner below block the al- ofof the end frame. lowablethe end frame.one, and the most stressed point is the one next to the lower right corner block of the end frame. Longitudinal Stiffness Longitudinal Stiffness LongitudinalWe constrained Stiffness the tank container by the lower corner blocks and applied the load of 75,000We constrained N to each of the the tank four container upper-corner by the blocks lower in corner the longitudinal blocks and applied direction. the Then, load We constrained the tank container by the lower corner blocks and applied the load weof 75,000 examined N to theeach nodal of the displacements four upper-corner identiﬁed blocks in in the the highest longitudinal point ofdirection. contact Then, between we of 75,000 N to each of the four upper-corner blocks in the longitudinal direction. Then, we theexamined frame andthe nodal the upright. displacements They have identified an average in the value highest of 14 point mm, whichof contact compared between to thethe examined the nodal displacements identified in the highest point of contact between the realframe one and of the 15 mmupright. gives They an error have ofan 6.6% average (Figure value 16 of). 14 The mm, equivalent which compared stress according to the real to frameVonone Misesof and 15 mm the (Figure upright.gives 17 an) assumes They error have of a 6.6% maximum an average(Figure value value16). atThe of the 14equivalent highest mm, which point stress compared of according the plate-upright to the to Vonreal oneattachment, of 15 mm equal gives to an 0.273 error· 10 of9 N/m6.6% 2(Figure, which, 16). albeit The slightly, equivalent exceeds stress the according allowable to stress. Von

MachinesMachines 2021 2021, 9, ,9 x, xFOR FOR PEER PEER REVIEW REVIEW 1414 of of 21 21

Machines 2021, 9, 44 14 of 21 MisesMises (Figure (Figure 17) 17) assumes assumes a a maximum maximum value value at at the the highest highest point point of of the the plate-upright plate-upright atat- tachment,tachment, equal equal to to 0.273 0.273 ∙ ∙10 109 9N/m N/m2,2 ,which, which, albeit albeit slightly, slightly, exceeds exceeds the the allowable allowable stress. stress.

FigureFigureFigure 16. 16.16. Nodal NodalNodal displacements. displacements.displacements.

FigureFigureFigure 17. 17.17. Equivalent EquivalentEquivalent stress stressstress (Von (Von(Von Mises). Mises).

TheTheThe normal normalnormal stress stressstress and andand bending bendingbending stress stressstress of ofof the thethe frame frameframe beams beamsbeams assumes assumesassumes a aa maximum maximummaximum value value equalequalequal to toto that thatthat allowable allowableallowable in inin the thethe central centralcentral area areaarea of ofof the thethe two twotwo upper upperupper end endend crosspieces; crosspieces;crosspieces; this thisthis is isis certainly certainlycertainly becausebecausebecause the thethe octagonal octagonaloctagonal plates platesplates welded weldedwelded to toto them themthem inin in that that area area make make them them very very stiff. stiff.

9.9.9. Carriage CarriageCarriage Anchoring AnchoringAnchoring Simulation SimulationSimulation The base of the frame of the model was constrained in such a way as to reproduce the TheThe base base of of the the frame frame of of the the model model was was constrained constrained in in such such a a way way as as to to reproduce reproduce anchorage to a carriage of a freight train. Then, we inserted a volumetric element inside thethe anchorage anchorage to to a a carriage carriage of of a a freight freight train. train. Then, Then, we we inserted inserted a a volumetric volumetric element element inin- the surfaces making up the tank, which, suitably generated and then meshed with solid45 sideside the the surfaces surfaces making making up up the the tank, tank, which, which, suitably suitably generated generated and and then then meshed meshed with with elements. Deﬁning R as the maximum gross mass equal to 36,000 kg and T as the tare of solid45 elements. Defining R as the maximum gross mass equal to 36,000 kg and T as the thesolid45 tank elements. container, Defining the inserted R as volume the maximum is that of gross the mass mass (R–T), equal which,to 36,000 together kg and with T as thethe taretaretare of ofof the thethe tank tanktank container, container, hasthe the inserted toinserted be submitted volume volume tois is athat that deceleration of of the the mass mass equal (R–T), (R–T), to 2which, which, g, to verify together together the withstresseswith the the duetare tare toof of thethe the consequenttank tank container, container, inertia has has forces to to be be thatsubmitted submitted arise. The to to a resultsa deceleration deceleration showthat equal equal the to to average 2 2 g, g, to to verifyofverify the the nodalthe stresses stresses displacements due due to to the the (Figureconsequent consequent 18) in inertia inertia the indicated forces forces that that points arise. arise. is The The equal results results to 3.4 show show mm, that that which, the the averagecomparedaverage of of the withthe nodal nodal the realdisplacements displacements value of 4 (Figure mm,(Figure gives 18) 18) in anin the errorthe indicated indicated of 15%. points points The equivalentis is equal equal to to 3.4 stresses, 3.4 mm, mm, which,accordingwhich, compared compared to Von Miseswith with (Figurethe the real real 19 value value), are of belowof 4 4 mm, mm, those gives gives allowable an an error error for of bothof 15%. 15%. materials The The equivalent equivalent used, the stresses,maximumstresses, according according value found to to Von Von is inMises Mises correspondence (Figure (Figure 19), 19), are withare below below the plate–skirt those those allowable allowable connection, for for both both in materials thematerials valve used,area,used, butthe the equallymaximum maximum high value value values found found occur is is in in correspon the correspon lateraldence areadence of with with the octagonalthe the plate–skirt plate–skirt plate. connection, connection, in in thethe valve valve area, area, but but equally equally high high values values occur occur in in the the lateral lateral area area of of the the octagonal octagonal plate. plate.

MachinesMachinesMachines 2021 20212021,, ,9 99,, ,x 44x FOR FOR PEER PEER REVIEW REVIEW 1515 of of 21 21

FigureFigure 18. 18. Nodal Nodal displacements. displacements.

FigureFigure 19. 19. Equivalent Equivalent stresses stresses (Von (Von Mises). Mises).Mises). On the corner supports, as regards the normal stress and bending stress of the frame OnOn the the corner corner supports, supports, as as regards regards the the norm normalal stress stress and and bending bending stress stress of of the the frame frame beams, we noted the greatest value. beams,beams, we we noted noted the the greatest greatest value. value. 10. Dynamic Analysis of Tank Containers for Foodstuff 10.10. Dynamic Dynamic Analysis Analysis of of Tank Tank Containers Containers for for Foodstuff Foodstuff The dynamic analysis [33,34] of the considered structure was performed, and two casesTheThe were dynamicdynamic examined: analysisanalysis [33,34][33,34] ofof thethe consconsideredidered structurestructure waswas performed,performed, andand twotwo cases were examined: 1.cases Emptywere examined: tank; 1.2.1. EmptyEmptyTank full tank; tank; of water.

2.2. TankInTank the full full ﬁrst of of case,water. water. we evaluated the deformations and the natural frequencies relative to theInIn ﬁrst thethe 10firstfirst modes case,case, ofwewe vibrations. evaluatedevaluated Forthethe thisdeformatdeformat analysis,ionsions it andand was thethe necessary naturalnatural tofrequenciesfrequencies furnish two relativerelative other toquantitiesto the the first first 10 that10 modes modes characterize of of vibrations. vibrations. the material, For For this this such analysis, analysis, as the it densityit was was necessary necessary and Poisson’s to to furnish furnish ratio. two two other other 3 quantitiesquantitiesThese that that values characterize characterize are for steel: the the material, densitymaterial,ρ such =such 7850 as as kg/mthe the density density; Poisson’s and and Poisson’s Poisson’s ratio υ = ratio. 0.3.ratio. TheseTheThese tank values values container are are for for was steel: steel: constrained density density ρ ρ = as= 7850 7850 in the kg/m kg/m case33; ;Poisson’s ofPoisson’s road transport ratio ratio υ υ = = with 0.3. 0.3. trucks, with a hingeTheThe intank tank each container container of the two was was lower constrained constrained corner as blocksas in in the the of case case the of frame,of road road whiletransport transport in the with with remaining trucks, trucks, with with two lower ones of the other frame with two carriages arranged to prevent longitudinal and aa hingehinge inin eacheach ofof thethe twotwo lowerlower cornercorner blocblocksks ofof thethe frame,frame, whilewhile inin thethe remainingremaining twotwo vertical displacement. We collected the values of the natural frequencies of vibrations, in lowerlower onesones ofof thethe otherother frameframe withwith twotwo carrcarriagesiages arrangedarranged toto preventprevent longitudinallongitudinal andand Hertz, and they are presented in Table7. verticalvertical displacement.displacement. WeWe collectedcollected thethe valuesvalues ofof thethe naturalnatural frequencfrequenciesies ofof vibrations,vibrations, inin Hertz,Hertz, and and they they are are presented presented in in Table Table 7. 7.

Machines 2021, 9, 44 16 of 21

Table 7. Case 1: Values of the natural frequencies of vibrations, in Hertz- empty tank.

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 3.54 12.27 18.99 25.79 26.22 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10 27.23 30.44 30.52 32.43 32.57

In the second dynamic analysis, we examined the water-ﬁlled tank, and the data results are reported in Table8

Table 8. Case 2: Natural frequencies tank water ﬁlled.

MODE 1 MODE 2 MODE 3 MODE 4 MODE 5 1.847 2.752 3.623 3.923 3.925

11. Discussion By mean the analysis of the obtained data results, it was possible to note that the FEM model created is substantially faithful to reality, especially as far as it concerns the frame. Data results comparison In Table9, the values obtained by experimental tests (Real Value) and numerical simulations (FEM Value) are reported.

Table 9. Comparison between the results provided by the manufacturer and those resulting from the FEM analysis.

Real Values FEM Value Error N◦ TEST Element (mm) (mm) % Ux = 0.66 0.58 12% 1 stacking Upright Uy = 2.15 2.0 7% Uz = 0.42 0.18 57% tank Usum = 2.0 1.0 50% 2 Top Lift spar Usum = 1.8 1.8 0% tank Usum = 1.6 0.8 50% 3 Lower Lift spar Usum = 1.5 1.6 6% 4 Transverse Stiffness Upright Usum = 3.0 2.4 20% 5 Longitudinal stiffness Upright Usum = 15.0 14.0 7% 6 Restraint Upright Usum = 4.0 3.4 15%

It is possible to note that, for the stacking test, the percentage maximum error is 57% for Uz, while for Ux and Uy, the percentages are 12% and 7%, respectively. For the Top Lift test, the spar element presented a negligible error, while for the tank element, the percentage maximum error is 50%. For the Lower Lift test, the spar element presented a percentage error of 6%, while for the tank element, the percentage maximum error is 50%. For the Transverse Stiffness test, the upright element presented a percentage error of 20%. For the longitudinal Stiffness test, the upright element presented a percentage error of 7%. For the Restraint test, the upright element presented a percentage error of 15%, Therefore, only for the upright element during the stacking test we detected, for Uz value, a big difference (57%), as well as for the tank element during the top and lower lift test (50%). Machines 2021, 9, 44 17 of 21

For the Dynamic Analysis of Tank Containers, it was possible to note the following: Case 1: From the analysis of the results, it is immediately evident how mode 1 of vibrating is the one that distances itself from the others in a greater way for the value of the natural frequency, equal to 3.54 Hz; in fact, Mode 2 has a value of 12.67 Hz and the third of 18.99 Hz. Case 2: From the analysis of the typical deformations relating to the first five modes of vibrations, it is possible to note a decrease in the system natural frequencies, and this is justifiable if we consider that, without prejudice to all the other geometric and material parameters of the tank container, the inertia of the system is greater. It is therefore evident that the dynamic response of the tank container changes depending on whether the tank is empty or full. The results of the first analysis can therefore be taken as a reference in the event that the tank container is transported empty or at the limit, and filled with a fluid with a low specific weight; instead, the last analysis can be useful in the opposite case. In order to adopt strategies to improve the response of the structure to the forcing actions coming from the roughness of the ground, one should know the estimated value of these frequencies, which are related to the profile of the soil and the speed of travel of the means of transport. A further forcing cause may be the so-called sloshing of the liquid inside the tank, so much so that there are rules that regulate the filling percentage of a tank container. This percentage must be greater than 80% or less than 20% of the total volume available.

12. Improvements Made to the Tank Container On the basis of the study carried out, in order to improve the performance of the tank container considered, changes were made for the parts that, from the FEM analysis, were found to be more stressed. In particular, the possibility of modifying the attachment points to the frame of the corner supports was studied, by at ﬁrst keeping their inclination constant, and then varying it in an appropriate range of values; subsequently, the thicknesses that characterize the components of the frame were changed, particularly on that of the octagonal plate and the skirt. All of this was done to determine a combination of these parameters that allows, at least for the same weight, a better response to the extreme stresses to which the tank container is submitted in the ISO tests, in particular for the longitudinal rigidity, which is the most burdensome for the tank container. For the considered model, the following hypotheses were made for the identiﬁcation of the displacements and the stress-state: 1. Purely elastic deformations and absence of breaks, 2. Perfectly isotropic and homogeneous materials, 3. Length of the elements, such as to ensure that the edge effects are negligible, 4. No thermal expansion. The tests were performed, maintaining constant the characteristics of the following: (a) Spar and upright; (b) End crosspiece; (c) Tank. Instead, the following geometric parameters were alternatively changed: (1) Thickness of the octagonal endplate, in the range (0.015 ÷ 0.020 m), (2) Thickness of the skirt, included in the interval (0.035 ÷ 0.045 m), (3) Displacement of the corner supports, with a constant angle, (4) Angle supports inclination, included in the interval (30◦ ÷ 45◦). Keeping the angle of 30◦ constant, starting from the displacement of the corner supports, an increasing reduction of the maximum equivalent stress was found due to the longitudinal stiffness test, which was 0.273 × 109 N/m2, and it reached a value of 0.189 × 109 N/m2 in the contact area between the upright and frame, in which the con- Machines 2021, 9, x FOR PEER REVIEW 18 of 21

(4) Angle supports inclination, included in the interval (30° ÷ 45°). Keeping the angle of 30° constant, starting from the displacement of the corner supports, an increasing reduction of the maximum equivalent stress was found due to the Machines 2021, 9, x FOR PEER REVIEW 9 2 18 of 21 longitudinal stiffness test, which was 0.273 × 10 N/m , and it reached a value of 0.189 × 109 N/m2 in the contact area between the upright and frame, in which the connection with the upright is at a height of 1.2 m, while with the spar it is equal to 2.4 m (Figure 20). (4) ForAngle the supports normal stress inclination, and bending included stress in theof the interval beams, (30° the ÷ speech 45°). is the same, as there Machines 2021 9 , , 44 is a reductionKeeping thein the angle maximum of 30° constant, equivalent starting stress, from identified the displacement in the upper of endthe cornercrosspiece,18 sup- of 21 whichports, anassumes increasing a value reduction of 0.131 of× 10 the9 N/m maxi2 againstmum equivalent the previous stress 0.240 was × 10found9 N/m due2. to the longitudinalReducing stiffness the thickness test, which of the was plate 0.273 and × the 109 skirtN/m by2, and 5 mm, it reached we obtain a value that ofthe 0.189 value × of10nection 9the N/m maximum2 with in the the contact equivalent upright area is betweenstress at a height increases theof upright 1.2 up m, to and whilea value frame, with of in0.218 the which spar × 10 the it9 N/mis connection equal2 (Figure to 2.4 with 21), m asthe(Figure well upright as 20 the). is normalat a height and of bending 1.2 m, whilestress. with the spar it is equal to 2.4 m (Figure 20). For the normal stress and bending stress of the beams, the speech is the same, as there is a reduction in the maximum equivalent stress, identified in the upper end crosspiece, which assumes a value of 0.131 × 109 N/m2 against the previous 0.240 × 109 N/m2. Reducing the thickness of the plate and the skirt by 5 mm, we obtain that the value of the maximum equivalent stress increases up to a value of 0.218 × 109 N/m2 (Figure 21), as well as the normal and bending stress.

FigureFigure 20. 20. MaximumMaximum equivalent equivalent tension. tension. For the normal stress and bending stress of the beams, the speech is the same, as there is a reduction in the maximum equivalent stress, identiﬁed in the upper end crosspiece, which assumes a value of 0.131 × 109 N/m2 against the previous 0.240 × 109 N/m2. Reducing the thickness of the plate and the skirt by 5 mm, we obtain that the value of the maximum equivalent stress increases up to a value of 0.218 × 109 N/m2 (Figure 21), as Figurewell as 20. the Maximum normal andequivalent bending tension. stress.

Figure 21. Maximum equivalent tension reducing the thickness of the plate and the skirt by 5 mm.

By trying to change the inclination from 30° to 45°, while maintaining the same attachment on the upright, we obtained a maximum stress value of 0.243 109 N/m2 (Figure 22).

FigureFigure 21. MaximumMaximum equivalent equivalent tension tension reducing reducing the thickness of the plate and the skirt by 5 mm.

By trying to change the inclination from 30◦ to 45◦, while maintaining the same By trying to change the inclination from 30° to 45°, while maintaining the same at- attachment on the upright, we obtained a maximum stress value of 0.243 · 109 N/m2 9 2 tachment(Figure 22 on). the upright, we obtained a maximum stress value of 0.243 10 N/m (Figure 22). The data results obtained indicated that the 30◦ position was the best. In summary, with these changes, we reduced the maximum tension in the longitudinal stiffness test, increasing the transverse one, but in a balanced way, as this too does not exceed the allowable stress. We obtained, in addition, an overall weight reduction of 55 kg, Machines 2021, 9, 44 19 of 21 Machines 2021, 9, x FOR PEER REVIEW 19 of 21

resulting from the algebraic sum of the reduction in the thickness of the plate and skirt and the increaseThe data in results the length obtained of the indicated supports. that the 30° position was the best.

Figure 22. ConditionCondition with maximum stress value. 13. Conclusions In summary, with these changes, we reduced the maximum tension in the longitudi- This study made it possible to evaluate the behavior of a tank container for foodstuff. nal stiffness test, increasing the transverse one, but in a balanced way, as this too does not By comparing the results obtained from experimental tests and numerical simulations, it exceed the allowable stress. We obtained, in addition, an overall weight reduction of 55 was possible both to validate the numerical model considered and to determine the areas kg, resulting from the algebraic sum of the reduction in the thickness of the plate and skirt with the highest equivalent stress and quantify the maximum value by comparing it with andthe allowablethe increase stress. in the In length this way, of the we supports. achieved a better understanding of the structure and detected that the most stressed area is that of the connections between the container and 13.the Conclusions frame [35,36]. The developed FEM model could be used for the following purposes: - ThisAllowing study changes made it inpossible the design to evaluate phase of the the behavior tank container, of a tank in relationcontainer to thefor foodstuff. responses By comparingof the model the results during obtained the ISO tests,from experi in suchmental a way tests as toand facilitate numerical their simulations, overcoming, it was possiblewithout both however to validate exceeding the numerical with oversizing. model considered and to determine the areas with- Optimizingthe highest equivalent the model bystress aiming and atquantify a significant the maximum reduction value in the by weight comparing of the chassis,it with the allowablewhich would stress. entail In this the way, possibility we achiev ofed increasing a better theunderstanding transport payload of the structure without and any detectedadditional that the cost. most stressed area is that of the connections between the container and the frameA more [35,36]. in-depth The developed study should FEM be model performed could in be the used future, for the with following the optimization purposes: of -the frame.Allowing The changes classic solution in the design is the one phase that of uses the objective tank container, functions. in relation to the re- sponsesThe limit of of the this model approach, during which theoperates ISO tests, by in means such ofa way discretization, as to facilitate is a considerable their over- amountcoming, of calculations; without however the greater exceeding they are, with the oversizing. greater the discretization is. The sensitivity -analysis Optimizing aims to identifythe model the by contributions aiming at a significant given by various reduction parameters in the weight that characterizeof the chas- the structuresis, which in would terms entail of strength the possibility and weight, of increasing providing the design transport indications payload capable without to obtainany less additional generous, cost. but more accurate sizing, which is better suited to stress problems detected by the tank container examined [37–39]. A more in-depth study should be performed in the future, with the optimization of theAuthor frame. Contributions: The classic A.L.,solution A.F., is A.P. the andone F.V.that equally uses objective contributed functions. to carrying out the research, whoseThe results limit are of reported this approach, in this work. which All authorsoperates have by readmeans and of agreed discretization, to the published is a consider- version of ablethe manuscript. amount of calculations; the greater they are, the greater the discretization is. The sen- sitivityFunding: analysisThis research aims receivedto identify no externalthe contri funding.butions given by various parameters that characterize the structure in terms of strength and weight, providing design indications capa- Data Availability Statement: Not applicable. ble to obtain less generous, but more accurate sizing, which is better suited to stress prob- lemsConflicts detected of Interest: by theThe tank authors container declare examined no conflict [37–39]. of interest.

Author Contributions: A.L., A.F., A.P. and F.V. equally contributed to carrying out the research, whose results are reported in this work. All authors have read and agreed to the published version of the manuscript.

Machines 2021, 9, 44 20 of 21

References 1. Bahreini Toussi, I.; Kianoush, R.; Mohammadian, A. Numerical and Experimental Investigation of Rectangular Liquid-Containing Structures under Seismic Excitation. Infrastructures 2021, 6, 1. [CrossRef] 2. Li, J.-Q.; Myoung, N.-S.; Kwon, J.-T.; Jang, S.-J.; Lee, T. A Study on the Prediction of the Temperature and Mass of Hydrogen Gas inside a Tank during Fast Filling Process. Energies 2020, 13, 6428. [CrossRef] 3. Batarliene, N. Essential Safety Factors for the Transport of Dangerous Goods by Road: A Case Study of Lithuania. Sustainability 2020, 12, 4954. [CrossRef] 4. Sasaki, N.; Kuribayashi, S.; Fukazawa, M.; Atlar, M. Towards a Realistic Estimation of the Powering Performance of a Ship with a Gate Rudder System. J. Mar. Sci. Eng. 2020, 8, 43. [CrossRef] 5. Wilson, J. The Model Railroader’s Guide to Intermodal Equipment & Operations. In Kalmbach Books; Kalmbach Pub Co.: Waukesha, WI, USA, 1999. 6. Frosina, E.; Senatore, A.; Andreozzi, A.; Fortunato, F.; Giliberti, P. Experimental and Numerical Analyses of the Sloshing in a Fuel Tank. Energies 2018, 11, 682. [CrossRef] 7. Zhao, J.; Zhu, X.; Wang, L. Study on Scheme of Outbound Railway Container Organization in Rail-Water Intermodal Transporta- tion. Sustainability 2020, 12, 1519. [CrossRef] 8. Formato, A.; Guida, D.; Ianniello, D.; Villecco, F.; Lenza, T.L.; Pellegrino, A. Design of Delivery Valve for Hydraulic Pumps. Machines 2018, 6, 44. [CrossRef] 9. Casdorph, D.G. Tank Containers USA (Transport History Monograph); Society of Freight Car Historians: Monrovia, CA, USA, 1994. 10. Jane’s Information Group. Jane’s Intermodal Transportation 1996–97: Efficient Information on the Worldwide Freight Business, 28th ed.; Jane’s Information Group: London, UK, 1996. 11. Casdorph, D.G. Intermodal Transport Pictorial and Review, No 2; Society of Freight Car Historians: Monrovia, CA, USA, 1994. 12. Casdorph, D.G. Evolution of Steel ISO Containers. Model Railr. 1998, 1, 30–33. 13. Eshraghi, S.; Carolan, M.; Perlman, B.; González, F. Comparison of methodologies for finite element model validation of railroad tank car side impact tests. ASME 2020, V001T15A001. [CrossRef] 14. Naviglio, D.; Formato, A.; Scaglione, G.; Montesano, D.; Pellegrino, A.; Villecco, F.; Gallo, M. Study of the Grape Cryo-Maceration Process at Different Temperatures. Foods 2018, 7, 107. [CrossRef] 15. Jamalabadi, M.Y.A. Optimal Design of Isothermal Sloshing Vessels by Entropy Generation Minimization Method. Mathematics 2019, 7, 380. [CrossRef] 16. Manca, A.G.; Pappalardo, C.M. Topology optimization procedure of aircraft mechanical components based on computer-aided design, multibody dynamics, and finite element analysis. In Proceeding of the 3rd International Conference on Design, Simulation, Manufacturing: The Innovation Exchange (DSMIE 2020), Kharkiv, Ukraine, 9–12 June 2020; pp. 159–168. 17. Formato, G.; Romano, R.; Formato, A.; Sorvari, J.; Koiranen, T.; Pellegrino, A.; Villecco, F. Fluid–Structure Interaction Modeling Applied to Peristaltic Pump Flow Simulations. Machines 2019, 7, 50. [CrossRef] 18. De Simone, M.C.; Guida, D. Experimental investigation on structural vibrations by a new shaking table. In Proceedings of the 24th Conference of the Italian Association of Theoretical and Applied Mechanics, (AIMETA 2019), Rome, Italy, 15–19 September 2019; pp. 819–831. 19. Aguiar De Souza, V.; Kirkayak, L.; Suzuki, K.; Ando, H.; Sueoka, H. Experimental and numerical analysis of container stack dynamics using a scaled model test. Ocean. Eng. 2012, 39, 24–42. [CrossRef] 20. Isler, C.A.; Asaff, Y.; Marinov, M. Designing a Geo-Strategic Railway Freight Network in Brazil Using GIS. Sustainability 2021, 13, 85. [CrossRef] 21. Uddin, M.; Huynh, N. Model for Collaboration among Carriers to Reduce Empty Container Truck Trips. Information 2020, 11, 377. [CrossRef] 22. Formato, A.; Ianniello, D.; Romano, R.; Pellegrino, A.; Villecco, F. Design and Development of a New Press for Grape Marc. Machines 2019, 7, 51. [CrossRef] 23. Goldschmidt, M.Z.; Jonson, M.L.; Horn, J. Tonal Noise Reduction for a Maneuverable Marine Hydrokinetic Cycloturbine Vehicle Using Turbine Clocking. J. Vib. Acoust. 2021, 143.[CrossRef] 24. Formato, A.; Ianniello, D.; Pellegrino, A.; Villecco, F. Vibration-Based Experimental Identification of the Elastic Moduli Using Plate Specimens of the Olive Tree. Machines 2019, 7, 46. [CrossRef] 25. Liu, X.; Yue, S.; Lu, L. A new method for optimizing the preheating characteristics of storage tanks. Renew. Energy 2021, 165, 25–36. [CrossRef] 26. Ahmadvand, M.; Asadi, P. Free vibration analysis of flexible rectangular fluid tanks with a horizontal crack. Appl. Math. Model. 2021, 91, 93–110. [CrossRef] 27. Ližbetin, J.; Stopka, O. Application of Specific Mathematical Methods in the Context of Revitalization of Defunct Intermodal Transport Terminal: A Case Study. Sustainability 2020, 12, 2295. [CrossRef] 28. Bao, B.; Wang, Q. A rain energy harvester using a self-release tank. Mech. Syst. Signal Process. 2021, 147, 107099. [CrossRef] 29. Wang, L.; Zhu, X. Container Loading Optimization in Rail–Truck Intermodal Terminals Considering Energy Consumption. Sustainability 2019, 11, 2383. [CrossRef] Machines 2021, 9, 44 21 of 21

30. Pappalardo, C.M.; Guida, D. An inverse dynamics approach based on the fundamental equations of constrained motion and on the theory of optimal control. In Proceedings of the 24th Conference of the Italian Association of Theoretical and Applied Mechanics (AIMETA 2019), Rome, Italy, 15–19 September 2019; pp. 336–352. 31. Tiernan, S.; Fahy, M. Dynamic FEA modelling of ISO tank containers. J. Mater. Process. Technol. 2002, 124, 126–132. [CrossRef] 32. Zhang, Z. A new measurement method of three-dimensional laser scanning for the volume of railway tank car (container). Measurement 2021, 170, 108454. [CrossRef] 33. Fomin, O.V.; Lovska, A.; Turpak, S.; Gorobchenko, O.M. Analysis of Dynamic Loading of Improved Construction of a Tank Container Under Operational Load Modes. EUREKA Physics Eng. 2019, 2, 61–70. [CrossRef] 34. Lovska, A.; Fomin, O.V.; Gerlici, J.; Kravchenko, K. Special Aspects of Determining the Dynamic Load of the Tank Container During Its Transportation in an Integrated Train Set by a Railway Ferry. In TRANSBALTICA XI: Transportation Science and Technology; Gopalakrishnan, K., Prentkovskis, O., Yatskiv, I., Juneviˇcius,R., Eds.; Springer: Cham, Switzerland, 2020; pp. 581–590. 35. Cho, I.H. Liquid sloshing in a swaying/rolling rectangular tank with a ﬂexible porous elastic bafﬂe. Mar. Struct. 2021, 75, 102865. [CrossRef] 36. Hur, S.-H.; Lee, C.; Roh, H.-S.; Park, S.; Choi, Y. Design and Simulation of a New Intermodal Automated Container Transport System (ACTS) Considering Different Operation Scenarios of Container Terminals. J. Mar. Sci. Eng. 2020, 8, 233. [CrossRef] 37. Kostrzewski, M.; Kostrzewski, A. Analysis of Operations upon Entry into Intermodal Freight Terminals. Appl. Sci. 2019, 9, 2558. [CrossRef] 38. Sicilia, M.; De Simone, M.C. Development of an Energy Recovery Device Based on the Dynamics of a Semi-trailer. In Proceedings of the 3rd International Conference on Design, Simulation, Manufacturing: The Innovation Exchange, (DSMIE 2020), Kharkiv, Ukraine, 9–12 June 2020; pp. 74–84. 39. Xing, L.; Xu, Q.; Cai, J.; Jin, Z. Distributed Robust Chance-Constrained Empty Container repositioning Optimization of the China Railway Express. Symmetry 2020, 12, 706. [CrossRef]