Final Project Description: Computer Aided Engineering

Due Date:

A report of the project and a presentation is due on December 4, 2003

Overview The overall guidelines for the final project is the combination of material discussed in class, in lab, and in this document.

The outline of material in this document is the expected outline for your project/report. Each section should discuss, in your own words, some of the material found in the various sections of this project description. Do not cut and paste these paragraphs in your report; but you should certainly make appropriate points in your project report that are made in the paragraphs below.

Final Project Goals The general goals of the final project are to complete the solid model of your ab-roller as well as to develop a finite element model of your ab-roller CAD model. The ab-roller will be modeled using various elements: beams, springs, shell and solid elements. Loads will be applied to the ab-roller (both a mechanical load to the handles and a gravity load), and a static analysis will be performed to determine the deflected shape and stress distribution in the supporting structure of the ab-roller. A final project report of this effort will be required as will a presentation. The report will include a description of: the CAD model and the process followed to make that CAD model, the FE modeling techniques used to model the various components of the ab-roller, the weights used for the various ab-roller components, the loads used in the model, the supporting boundary conditions, and finally the deflected shapes and stress results based on the loading. Various plots to help describe these detailed aspects of the FE modeling of the ab-roller will be expected as part of the report. More details for each of these areas can be found below.

Solid Model The CAD geometry will be discussed in class. The CAD model should be discussed, including the details in developing the model with corresponding plots of the various components. Any detailed dimensions or sketches of the ab-roller should be included in the report. The description of the solid model and the corresponding drawings and sketches should provide the reader with enough information to create the ab-roller from scratch using only your report. This description should also include details of the process that was followed to create the solid model. The detail level that is expected is the general command that was used in creating various features of the solid model (in general, the commands you can view in the history tree). The level of detail that includes literally every step that was performed is not expected or desired.

A finite element model is expected of the ab-roller. Since we are developing FE models of the various components of the ab-roller, it is important that the CAD model that is used for the basis of the FEM model should not contain unnecessary detail. For example, in your CAD model, you could have used fillets. It is highly recommended that small features (like fillets) be removed or suppressed from your “FEM geometry” model; the FEM geometry model is the solid model geometry that you are planning to use to develop your FEM model. You should note what geometry is suppressed or removed and discuss this in your report.

Wheels (Rollers)

The four wheels of the ab-roller should be modeled with solid elements (8 noded brick elements if the wheel is modeled with a hollow center core). A mapped mesh should be used. To reduce the number of nodes in the overall model and hence keep solution time to a minimum, it is recommended to use 2 elements in the radial direction, 3 elements in the circumferential direction over a 90 degree arch, and 2 elements in the axial direction (the thickness of the wheel or roller). The two elements in the axial direction (along with the three in the 90 degree direction) will guarantee a node on the plane of symmetry of the roller. This node will eventually be supported.

In order to get a node on the axis of the wheel so that it can be attached to the beam model of the axle (discussed below), the following procedure should be followed and discussed in your report. The first step is to get a node on the axis of each face of the wheel. This is easily achieved by using the “between nodes” command by choosing two nodes on the face of the wheel that are diametrically opposite. Once the center node is generated (say node 2002), the second step is to run “spider” beam elements from that node to the inner radius nodes on the face of that wheel. These spider beams can reference the x-sectional area property of the axle beam elements (discussed below), but their material ID MID) should reference an elastic modulus E that is 10**5 times larger than the axle’s MID. Essentially this spider element is modeling the center of the wheel as a rigid core. This approximation can be used if it is argued that the axle material fills the core to the wheel in a rigid-like manner, and accurate stresses in this area are not needed. The wheel’s ability to rotate about the axle will be modeled by using coincident nodes that are tied together with translational springs (discussed below).

Bullet As discussed in class, the main body of the ab-roller is bullet or torpedo in shape. This part of the ab-roller is a solid plastic material. In order to support and “house” the four wheels, the bullet has “aprons” or sides, that go down from the main body of the bullet to support the axle. These aprons, or tabs, or gusset plates, are shell-like structures and will be modeled as shell elements. These gusset plates will be modeled with a constant thickness 0.25 inches. The modeling of the gusset plates will be discussed in the next section.

It is highly recommended that the two models of the bullet and gusset plate be joined together using a Boolean “join” command. Once the two parts are joined together to form one part, the gusset plate should be partitioned from the solid “core” section of the bullet. The partitioning plane should be chosen such that the geometry above the plane is “solid like”, and the geometry below the plane is “shell like”. A plot should be generated showing where that plane partition was taken. Once this section is partitioned, a solid mesh of the bullet should be generated as discussed in the next paragraph.

As discussed earlier, make sure the small dimensions (fillets, etc.) are suppressed or deleted before generating a solid tetra mesh for the bullet. It is recommended that an element length of approximately 0.5 inches be used. The pointed nose of the bullet should also be partitioned out of the solid model. The bullets nose should be “cut off” or partitioned such that the resulting nose diameter is approximately 0.5 inches.

Since the handles will be modeled with beam elements (see below), the actual connection between the handle’s beam element and the bullet will be at one node for each handle. Hence it is recommended that the detail of the handle’s connection into the bullet be suppressed when generating nodes and elements for the bullet. While one might use an “anchor point” to generate a node exactly where the handle would attach, it is not necessary since a node will be generated “close enough” to the handle’s attachment to the bullet.

A linear tetra mesh should be generated. Make sure the poor performance of the tetras is discussed in your report, and explain that the linear tetras were chosen because they would reduce the size of the problem. Time permitting and resources permitting, the problem can be re-run using parabolic tetras (which will cause the need of parabolic shells for the gusset plates). These parabolic runs should only be done after complete checkout of the linear model runs. The parabolic runs are not required.

Gusset Plate A shell mesh should be generated on the outer surface of the gusset plate. The element size should be chosen as 0.5 inches to be consistent with the size elements in the bullet. Before the mesh is generated, “anchor points” should be generated on the surface at the axial location of each axle. This will cause nodes to be generated at the axial location on the gusset plate. These nodes will be nodes that the axle, modeled as beam elements, will be attached to.

One of the problems of connecting a shell element to a solid element is that there is a “hinge line” along the line connecting the two elements. This means no moment (about the line connecting each element) can be transferred across the boundary. Since the gusset plate does transfer moment into the bullet, a plan must be in place to transfer this moment. This can be achieved by placing shell elements on an adjacent face of the solid where the shell is attached to the solid nodes. The easiest way to achieve this is to place shell elements on the planer surface that partitions the bullet solid region from the gusset region. These shells can have the same thickness as the other shell elements. These shells should reference a MID that has the same elastic properties as the other shells, but will eventually be assigned a density of 0.0 since its use is only to transfer moment.

Axle The axle is assumed to be a 0.5 inch diameter beam element. It will be modeled using the same basic material as the rest of the ab-roller (discussed below). The axle will go from one node on one gusset plate to the symmetric node on the other gusset plate. Instead of using one beam element between those two nodes, three beam elements should be used that connect up four nodes on the axle: the ones on each gusset plate and two new ones that are geometrically on the face of the each wheel but not directly attached to the wheel. For example, assume the four nodes on the axle along its axis are nodes 1001, 1002, 1003, and 1004, where 1001 and 1004 are on the gusset plates and 1002 and 1003 are on the face of each wheel. The three beam elements representing the continuous axle are between nodes 1001-1002, 1002-1003, and 1003-1004. Let’s also assume that the wheel (or roller) discussed above has nodes 2002 and 2003, which are nodes on each face of the wheel. These nodes (2002 and 2003) are directly attached to the wheel by using the spider beam elements discussed earlier. Nodes 2002 and 2003 are coincident to nodes 1002 and 1003, respectively. The wheel will be attached to the axle using the spring elements discussed below.

Axle-Roller Connection (spring) The wheel or roller is attached to the axle by using stiff spring elements. The springs only connect the translational degrees of freedom x, y, and z (DOF s 1,2, & 3) of node 1002 to node 2002 and node 1003 to node 2003. If a large value for the spring stiffness is used, the translational degrees of freedom of the coincident nodes will be tied together. This will act like a ball and socket joint, and the combination of these ball and sockets on opposing faces will allow for rotation of the wheel about its axial direction relative to the bullet (any other relative translation or relative rotation of the wheel and the bullet is not allowed via this connection).

It is recommended that the stiffness of these springs be 10**5 times bigger than the local stiffness. A trail stiffness value of 1.0E5 lb/in should be chosen. A larger value can be considered if there is any relative translational motion between the coincident nodes.

Handles The handles are to be modeled using beam elements. The handles have a x-section that varies along the length of the handle. Either of the two following beam models can be used for the handle.

A detailed beam model for the handle can be created by saving the x-sections of the handle at 5 locations along its axis. These x-section locations are at either end of the handle as well as the ¼ points and mid-point of the handle. Using a non-prismatic beam element, each end of each of the four beams can reference the appropriate x-section.

A simple beam model of the handle is also acceptable. Using one of the available x- sections offered in MS (for example, an elliptical x-section), a beam with a constant x- section can be used. The x-section should approximately match the section where the handle connects to the bullet. At least two beam elements should be used so that there is a node at the middle of the handle at which the loading can be applied. Where the handle’s beam elements attach to a node of the bullet, only translational forces can be transferred to such solid nodes (solid nodes only offer stiffness for translational degrees of freedom). Hence such a connection is a ball and socket connection. If moment is to be transferred (and there is a full load and moment transfer between the handle and the bullet), it is recommended that spider elements be used to connect the end node of the handle to several adjacent nodes of the bullet.

Complete FE model & Checking The overall finite element model can be put together in one assembled model using the procedures that have been outlined in class (appending FEM models together).

Once one FE model for a wheel-axle assembly is made, this can be copied using the “orient-copy” command. It can be copied 3 times to generate the other models of the wheels. This should be done only after one wheel assembly has been created and checked. For example, the solid model for the wheel should be created and checked (check free edges and coincident nodes). The spider elements should have been completed. The wheel’s attachment to the axial should have been completed via the springs, and the axial should be attached to the gusset plate. Then this entire assembly (the wheel solid elements, the spider beam elements, the axle beam elements, and the spring elements) can be copied 3 times to generate the other wheel assemblies. Once these elements have been copied, there will be 6 pairs of coincident nodes where the three just-copied axles connect to the shell elements of the gusset. These nodes, and only these nodes, must be merged so that these axles connect to the gusset shells.

Free edge plots and coincident node checks should also be conducted of the entire FEM model to check the model. Coincident nodes where each wheel connects to the axle should be expected and verified.

Weight, Materials and Property IDs

It is assumed that all material of the ab-roller has an elastic modulus of E = 4.0E6 psi and a Poisson’s ratio of 0.3. This includes the bullet, the gusset plate, the wheels, the axle, and the handles. Any elements that are rigid or used to spider loads are assumed to have properties that were discussed previously.

The various parts of the ab-roller are assumed to have the following weights:

101 Bullet 0.6 lbs = 0.6 lbs 102 Gusset 0.3 lbs (2 of these) = 0.6 lbs 103 Each Wheel and Axle combo 0.2 lbs (4 of these) = 0.8 lbs 104 Each handle 0.4 lbs (2 of these) = 0.8 lbs 105 Moment transfer shells = 0.0 106 Spider beam elements = 0.0

Total 2.8 lbs

This represents a total weight for the ab-roller of 2.8 lbs. The MIDs will be discussed below.

From a FE modeling point of view, each separate component modeled should have its own Material ID (MID) and, if needed, Property ID (PID). This will allow for some variability in choosing weights (and densities) of the various components. This will allow each group of the FE model to have the correct weight (hence the correct overall weight). An extremely important capability offered in Master Series must be used in this step: the ability to set up groups of elements, name those groups, and manipulate those groups.

Once all the elements have been created, referencing PIDs and MIDs that have been automatically created in Master Series, the following procedure is recommended.

1) Copy the MID 1 (it probably has steel properties) to MID 101. Modify MID 101 to have E = 4.0E6 psi, and nu = 0.3. For the time being, also modify its density to have a value of 1.0 units. These “units” will be discussed shortly. 2) Copy MID 101 five more times to MIDs 102, 103, 104, 105, and 106. These will be discussed shortly. 3) Modify all solid elements of the bullet to have a MID of 101. It is recommended that that be accomplished by creating a group of just the bullet tetra elements. Then compute the volume of these elements. Divide the weight of the bullet (0.6 lbs) by the volume of these elements, and compute a density. This density will be in lbs/in**3. Modify MID 101 to have this density. Compute the mass of these elements again, and verify the mass (now in lbs) should now be 0.6 lbs. 4) Group all the shell elements of the gusset together. Do not include in this group the shell elements that are on the bottom of the bullet which were used to transfer bending moments from the gusset to the bullet (these elements will be handled later). Modify these gusset elements to MID 102. Adjust the density of MID 102 (as in step 3) to get the correct weight of 0.6 lbs. 5) Group all axle and wheel solid elements (but not the spider beam elements for the wheel) as the wheel assembly. Modify the MID of these elements to MID 103. Adjust density of MID 103 (as in step 3) to get the correct weight of 0.8 lbs. Verify. 6) Group the beam elements of the handle together (once again, do not include the spider elements that were used to attach the beam to the bullet). Modify the MID of these elements to MID 104. Adjust density of MID 104 (as in step 3) to get the correct weight of 0.8 lbs. 7) Group together the shell elements that attach to the bottom of the bullet solid model. These elements are used to transfer the moment connection between the shell gussets and solids for the bullet. Modify the MID of these shells to MID 105. Set the density of MID 105 to 0.0 lbs/in**3. 8) Group together all the spider elements, including those of the wheel and those of the handle attachment to the bullet. Modify these elements to have MID 106. Modify MID 106 to have a density of 0.0. Modify the elastic modulus to be 10**5 times bigger than the 4.0E6 psi value that is already there (ie, 4.0E11 psi).

Next determine the weight of the overall FE model using all the elements. The total weight (in lbs) should be 2.8 lbs. Report this weight and its CG location.

Loads The basic loading on the ab-roller will be both a “subject” load and a gravity load (this will be supported by the base casters of the ab-roller). The subject load corresponds to a 200 lb person with a safety factor of 1.5. This yields a 300 lb load that is to be equally spilt between a person’s hands and knees as the ab-roller is used. Hence a total of 150 lbs is to be applied to the ab-roller, with 75 lbs to each handle. The 150 lb load should be applied vertically downward, and each 75 lbs can be applied to the center point of the handle or as a distributed line load along the beam elements of the handle.

The loading in Master Series should include the mechanical load of 150 lbs (75 lbs to each handle) and the gravitational load of 2.8 lbs. Hence the total load acting downward is 152.8 lbs, and this should be reflected in the supports.

With regard to the magnitude of the gravity vector, since the material density was used in lbs/in**3, the gravity vector should have a magnitude of 1.0 and not the usual 386.4 in/sec**2. This procedure is acceptable since we are not concerned with dynamic models. Otherwise the mass properties should be entered in mass/in**3 instead of weight/in**3, and the gravity vector should be 386.4 in/sec**2.

Support (Boundary Conditions) The ab-roller should be restrained at the apex node of each roller where that roller makes contact with the ground. This will result in one node for each wheel where the translational degrees of freedom are constrained.

As discussed in class, even with these degrees of freedom constrained, still un- constrained is an overall rigid body mode where the combined assembly can rotate about the line connecting the supported nodes. In addition, there is a mechanism that is also not constrained where the bullet section can move in its for-aft direction (as it rotates about the bottom of the wheels). Both the overall rigid body motion as well as the mechanism must be constrained to prevent a singular stiffness matrix. This can be achieved by taking a node on the bullet that is on the plane of symmetry, and constraining it both in the for- aft direction (the rolling direction) as well as in the cross direction (from one handle tip to the other). The constraint forces for each of these restraints should be zero (otherwise a mistake has been made). This should be checked when reviewing the restraint forces.

Analysis Results For the loading and boundary conditions presented, an analysis shall be performed to determine the deflections and stresses. Hand calculations of the total weight and its verification in the Model Solution run, using the reaction forces, shall be presented. For example, the CG location for the ab-roller can be determined by requesting the mass properties of the entire FEM model. Construct a 2-D free body diagram showing, looking along the handle direction, the 150 lb load, the gravity load of 2.8 lbs acting downward, and the 4 support forces. Verify that the sum of forces lateral and vertical add up to zero, and verify that the sum of moments about any point are zero. Show these calculations in your report. Verify that the total vertical load is 152.8 lbs.

Provide a stress Von-Mises plot of the stresses on the outer surface of the shell elements of the gusset plate. Show both sides in the plot, and discuss any lack of symmetry.

Show deformed plots of the ab-roller. Show the deformed shape in red, and the undeformed shape in green. Do not show any contours with these deformation plots. Show these deformation plots from orthogonal and isometric views. Provide any calculations that might verify the maximum deflection.

Discuss results including any lack of symmetry.