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Computer Program for the Calculation of Mindlin Plates BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS FACULTY OF CIVIL ENGINEERING COMPUTER PROGRAM FOR THE CALCULATION OF MINDLIN PLATES Scientific Student’s Association Thesis BENCE BALOGH Student, MSc in Computational Structural Engineering, BUTE Supervisor Dr. Imre Bojtár Department of Structural Mechanics, BUTE Budapest, 2013. Bence Balogh COMPUTER PROGRAM FOR THE CALCULATION OF MINDLIN PLATES To my grandmother. 2 Bence Balogh COMPUTER PROGRAM FOR THE CALCULATION OF MINDLIN PLATES PREFACE This thesis is about the making of a computer program capable of calculating rectangular Mindlin plates resting on elastic Winkler foundation. I devote the program to be helpful to the students and be a useful tool in the preliminary design of simple structures. To achieve these goals, my expectations towards the software are high calculation speed, self- explanatory graphical user interface and the ability to visualize the results in a clear manner. It is important that the program is free and it will be available for download at the web site of the Department of Structural Mechanics (http://www.me.bme.hu). The program is intended to provide solution of four section types, so in the first chapter I present the common mechanical models of these types of plates. The first type deals with isotropic homogeneous plates. In this context, I will detail first the classical Kirchoff and later introduce the Mindlin theory as an extension using first-order shear theory. The second type treats sandwich constructions. The third involves composite material plates including anisotropy and symmetrically laminated considerations while the last deals with plates including voids. After the theoretical introduction, in the second chapter I introduce the original solution of Professor Ernest Hinton* for rectangular isotropic plates based on Mindlin plate theory. The original code went beyond an overhaul, and this final version will be detailed. The program itself is constructed in FORTRAN computational language and provides solution for simply supported plates. The third section covers the making of the graphical user interface (GUI). For this task I have chosen the fully object oriented VISUAL BASIC .NET 4.5 as a programming environment. This part proved to have the biggest extent, so the reader can meet in more details with the different solution techniques and tricks. At the end of this chapter the numerical and graphical results of the program will be verified by finite element calculations. In the last chapter there is a short comparison of the created program with the leading inland civil engineering software, namely AXIS and FEM-Design. It is important to emphasize, that is was not between the goals of creating this program to produce a rival of these software, but to provide an easy way to get results very quickly in case of some simple plated structures. The standard educational routine does not include programming courses, therefore I find it to be a very important result, that through the thesis I managed to learn two different programming language from the bottom and this knowledge could be a useful tool in the future. 3 Bence Balogh COMPUTER PROGRAM FOR THE CALCULATION OF MINDLIN PLATES BEVEZETŐ Jelen munka tárgya egy olyan számítógépes program megírása, mely lehetővé teszi négyzet alaprajzú, csuklósan megtámasztott, rugalmasan megtámasztott lemezek számítását a Mindlin lemezelmélet szerint. A program készítésének célja, hogy hasznos eszköz legyen mind a hallgatóság, mind a gyakorló mérnökök kezében akár az előtervezés folyamatában. Hogy ezeket a célokat elérjem, előzetes elvárásaim a gyors futási idő, könnyen kezelhető grafikus felület és a látványos eredmény feldolgozás voltak. A program ingyenes, elkészültével letölthető lesz a Tartószerkezetek Mechanikája Tanszék honlapjáról (http://www.me.bme.hu). A program négy keresztmetszet típust támogat, az első fejezetben ezeknek a lemezeknek a szokásos mechanikai modelljeit mutatom be. Az első típus a homogén lemez, aminek kapcsán bemutatásra kerülnek a klasszikus Kirchoff, majd a Mindlin – Reissner lemezelmélet az előbbi kiterjesztéseként. A második típus a szendvics keresztmetszetű lemez. A harmadik szimmetrikusan laminált lemezekkel foglalkozik, az utolsó pedig az egyik irányban üreges lemezek számításának módját mutatja be. Az elméleti áttekintés után, a második fejezetben bemutatom Ernest Hinton megoldását. Az eredeti kód FORTRAN77 nyelven íródott, azonban a jelentős mértékű átalakítás miatt csak a végső, javított verziót közlöm. A harmadik fejezet bemutatja az elkészült grafikus felhasználói felületet. Ehhez a munkához az immár teljesen objektum orientált VISUAL BASIC .NET 4.5 programnyelvet választottam. Ez a munka bizonyult a legterjedelmesebbnek, ezért részletesebben bemutatásra kerülnek majd a különböző megoldások. A fejezet végén mind a numerikus, mind a grafikai eredmények verifikálásra kerülnek végeselemes számolások révén. Az utolsó fejezetben ismertetek egy szubjektív összehasonlítást az elkészült program és az ANSYS, valamint a vezető hazai építőmérnöki statikai méretező programok (Axis, FEM- Design) között a számítási idő tekintetében. Hangsúlyozom, hogy a program céljai között nem szerepelt, hogy felvegye a versenyt az említett szoftverekkel, ugyanakkor bizonyos egyszerű esetekben gyors és megbízható eredményre vezet. Végül megemlítem, hogy az építőmérnöki kari tanrend nem tartalmaz programozási kurzusokat, így a fent említett két programozási nyelvet önállóan tanultam meg, a megszerzett tudást pedig mindenféleképpen hasznosnak tartom a továbbiakban. 4 Bence Balogh COMPUTER PROGRAM FOR THE CALCULATION OF MINDLIN PLATES Table of Contents Table of Contents .................................................................................................................................... 5 Terminology............................................................................................................................................. 7 1. Plate theory ................................................................................................................................... 11 1.1. Kirchoff - Love plate theory ................................................................................................... 11 1.2. Mindlin - Reissner plate theory .............................................................................................. 17 1.3. Constitutive equations of laminated composite plates ......................................................... 20 1.4. Classical theory of laminated composite plates with small strains and small rotations ....... 30 1.5. Classical theory of laminated composite plates with small strains and moderate rotations 34 1.6. The first-order laminated plate theory with small strains and small rotations ..................... 36 1.7. Other theories for laminated composite plates .................................................................... 38 1.8. Theory of sandwich plates ..................................................................................................... 39 1.9. Theory of voided plates ......................................................................................................... 40 1.10. Plates on elastic foundation .................................................................................................. 41 2. Numerical solution ........................................................................................................................ 43 2.1. Theoretical background ......................................................................................................... 43 2.2. Computational solution ......................................................................................................... 50 2.2.1. Introduction ................................................................................................................... 50 2.2.2. Program details ............................................................................................................. 52 3. Graphical solution ......................................................................................................................... 69 3.1 Introduction to Visual Basic .NET ........................................................................................... 69 3.2 BENSYS Program structure..................................................................................................... 73 3.1.1. The splash form ............................................................................................................. 73 3.1.2. The Project Form ........................................................................................................... 76 3.1.3. The Main Form .............................................................................................................. 76 4. Verification .................................................................................................................................... 98 4.1. Verification of the load cases ................................................................................................. 98 4.2. Verification of the single layer models ................................................................................ 105 5. Outcome ...................................................................................................................................... 109 5.1. Comparison with other software ......................................................................................... 109 5.2. Future plans
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