Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 1989 Investigation of substructuring principles in the finite element analysis of an automotive space structure John E. Martin Follow this and additional works at: http://scholarworks.rit.edu/theses Recommended Citation Martin, John E., "Investigation of substructuring principles in the finite element analysis of an automotive space structure" (1989). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Investigation of Substructuring Principles in the Finite Element Analysis of an Automotive Space Structure JOHN E. MARTIN A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE ill Mechanical Engineering Rochester Institute ofTechnology Rochester, New York May 1989 Approved by: Dr. JOiSepb S. Torok (AdvisQr) Dr. Richard G. Budynas Dr. Hany Ghoneim Dr. Wayne W. Walter Dr. Bhalchandra V. Karlekar Professor and Department Head ACKNOWLEDGEMENTS This work is dedicated to my mother Ruth R. Martin, my father Edward L. Martin and my three siblings Chris, Sandy and Susan Martin. For the love, support, encouragement and constant diversions provided during the year that I have been researching and writing this thesis, thank you. To my advisor, Dr. Joseph S. Torok. You were always able to provide a kind word and smile when I needed it. Thank you for your support and encouragement on the thesis and other professional matters. To Dr. Hany Ghoneim, for his assistance when I was learning to use ANSYS. I deeply appreciate your words of encouragement. To Lam from Stress Technologies Incorporated. I just want you to know how much I Tony , appreciate your technical advice concerning ANSYS. My research would never have gone as smoothly as it did, without your assistance. "Samuel" To my friends, I-en Lin and Shashank Kolhatkar, who provided me with companionship and light diversions through all of this crazy time. Thanks for the fun. To the members of my thesis defense committee: Dr. Richard G. Budynas, Dr. Hany Ghoneim and Dr. Wayne Walter. Thank you for taking the time to study my work and make your comments and suggestions. Finally, I would like to thank my fellow members from the Rochester Chapter of NSA. You helped me find the strength and spiritual growth that I needed to face the challenges in my life. Thanks to you, I hope to go on and accomplish something remarkable with my life. ABSTRACT The efficiency of using substructuring in the dynamic analysis of small models is examined by using a university version of ANSYS to perform a series of four case studies on a small, 648 degree of freedom model. The model is based upon the monocoque center section for an automotive space structure and was constructed using STTF 63 plate elements. In each case study, the model was divided into a different substructure configuration. In the configurations used, the model was divided into one, two, three and four substructures, respectively. In each case study, a series of modal analyses was performed for different master degree of freedom configurations. The first four eigenvalues and the CPU time needed to find a solution were compared. Based upon numerical experiments, it is shown that dynamic substructuring has a great potential for saving CPU time. Optimal substructured solutions which resulted in natural frequencies that agree with the frequencies of a non-substructured baseline solution within a tolerance of three to four significant digits could be found for an appreciable (17.49-70.16 CPU seconds) savings in CPU time. It is also demonstrated that the number of master degrees of freedom placed along the substructure boundaries has the strongest effect upon solution efficiency. Minimizing the number of boundary master degrees of freedom is shown to minimize the amount of CPU time needed to find a solution with a desired level of accuracy. THESIS OUTLINE ABSTRACT TABLE OF CONTENTS CHAPTER 1 . INTRODUCTION TO SUBSTRUCTURING 1) Basic Concepts 2) Mathematical Theory CHAPTER 2. BACKGROUND/LITERATURE SEARCH CHAPTER 3. EXAMPLE PROBLEMS 1) ID Spring 2) 2D Truss CHAPTER 4. THE GENERAL METHOD OF SUBSTRUCTURING CHAPTER 5. SUBSTRUCTURING IN ANSYS 1) The Generation Pass 2) The Use Pass 3) The Stress Pass 4) Relating the Passes a) General File Handling b) Substructure Connectivity c) Combination of Post Processing Files (FILE 12) using /AUX1 d) Combining File Handling Commands into Run Files e) Master Degrees of Freedom - Finding the Totals CHAPTER 6. CASE STUDIES 1) Description of Problem Section of an a) Modal Analysis of the Monocoque Center Automotive Space Structure b) History c) Material ASTM 5052 Aluminum d) Other ii 2) Research a) One Substructure b) Two Substructures c) Three Substructures d) Four Substructures CHAPTER 7. CONCLUSIONS REFERENCES APPENDICES 1) ANSYS COMMANDS 2) ANSYS RUN FILES FOR THE FOUR CASE STUDIES BIBLIOGRAPHY ui TABLE OF CONTENTS PAGE LIST OF FIGURES v LIST OF TABLES - vii LIST OF SYMBOLS - viii CHAPTER 1. INTRODUCTION TO SUBSTRUCTURING - 1 CHAPTER 2. BACKGROUND / LITERATURE SEARCH 10 CHAPTER 3. EXAMPLE PROBLEMS 23 CHAPTER 4. THE GENERAL METHOD OF SUBSTRUCTURING 34 CHAPTER 5. SUBSTRUCTURING IN ANSYS 39 CHAPTER 6. CASE STUDIES 49 CHAPTER 7. CONCLUSIONS -- 82 REFERENCES-- 88 APPENDIX 1. ANSYS COMMANDS 90 APPENDIX 2. ANSYS RUN FILES FOR THE FOUR CASE STUDIES 100 IV LIST OF FIGURES FIGURE PAGE 1 . 1 Models Demonstrating the Flexibility of the Finite Element Method 2 1 .2 The Discretization of the Model into Substructures and of 3 Substructures into Elements 1 .3 A Graphic Explanation of the Master and Slave Degrees of Freedom 5 1.4 - A Discrete Dynamic System Model 8 2. 1 Schematic of the Boeing 747 with the Wing-Body Intersection 1 1 Highlighted 2.2 - Schematic of the Substructures used in the Analysis of the 12 Wing-Body Intersection of the Boeing 747 2.3 Finite Element Models of the Two Substructures Modeling 1 3 the Monocoque Center Section of the Boeing 747 2.4 Finite Element Models of the Two Substructures Modeling 14 the Wing Structure and Wheel Well Area of the Boeing 747 3.1 The Model for a ID Spring Substructuring Example Problem 24 3.2 The Model for a 2D Truss Substructuring Example Problem 29 4. 1 A Finite Element Grid Displaying the Two Kinds of Master 35 Degrees of Freedom, Boundary and Internal 4.2 Two Different Discretizations of the Plate Model Used in 36 the Case Studies 5.1 Row Chart Displaying the File Handling for a Generalized 41 Multiple Substructure Analysis 5.2 The Generalized Input Files for the Generation and Use Passes 44 5.3 The Generalized Input Files for the Stress Passes 45 5.4 A Method for Finding the TOTAL Values Shown - 48 with a Three-Substructure Model 6. 1 The Basic Monocoque Center Section and the Center Section 50 with Suspension Attachment Sections 6.2 Plots of the First Four Mode Shapes 51 6.3 A Table Displaying the Results of the Baseline Analyses 52 6.4 The Substructure Discretization for the Four-Substructure 55 Case Study 6.5 TOTAL Value Calculations for the Four-Substructure Case Study 56 6.6 Flow Chart Displaying the File Handling for the 58 Four-Substructure Case Study 6.7 The Substructure Discretization for the Three-Substructure 62 Case Study 6.8 TOTAL Value Calculations for the Three-Substructure Case Study 63 6.9 Row Chart Displaying the File Handling for the 65 Three-Substructure Case Study 6.10 The Substructure Discretization for the Two-Substructure 69 Case Study 6. 1 1 TOTAL Value Calculations for the Two-Substructure Case Study 70 6.12 Row Chart Displaying the File Handling for the 72 Two-Substructure Case Study 6.13 The Substructure Discretization for the One-Substructure 76 Case Study 6.14 Flow Chart Displaying the File Handling for the 77 One-Substructure Case Study 7. 1 Bar Graph of the CPU Times Needed to Analyze and Post - 85 Process Models Using the Optimum Master Degree of Freedom Configuration 7.2 Model Frequencies for the Master Degree of Freedom 86 Configurations of the Two-Substructure Case Study A. 1 Row chart Displaying the File Handling for the - 99 Sample Input File for /AUX1 module vi LIST OF TABLES TABLE PAGE 6. 1 Data for the Four-Substructure Case Study - - - 59 6.2 Data for the Three-Substructure Case Study 66 6.3 Data for the Two-Substructure Case Study 73 6.4 Data for the One-Substructure Case Study 78 VII LIST OF SYMBOLS A Cross Sectional Area Ad(v,p) Generalized Form of the Dirichlet Problem Ae Matrix used to find ALPHA in the Finite Element Solution of the Dirichlet Problem Ai Kss Matrix for Substructure i Ao Matrix Assembled out of the Kmm Matricies for all Substructures ALPHA Coefficient Vector used in Numerical Solution of Dirichlet Problem B Mode Shapes Related to Kron's Matrix BDOFi Number of Boundary Degrees of Freedom in Substructure i BETA Angle of Inclination of the General 2D Truss Element Bi Ksm Matrix for Substructure i Bp Preconditioning Matrix C Damping Matrix CDOFi Number of Constrained Degrees of Freedom in Substructure i Ci Kms Matrix for Substructure i Co Cosine of Angle of Inclination of Truss Element D Domain in Dirichlet Problem E Young's Modulus F(t) Dynamic Load Vector f(s) Spatial Distribution of Load in a Dynamic Equation the First Example Problem Fl F2 Forces Applied to Nodes 1 , 2, 3, 4 in F3F4 Fa Fb Fc Nodal Forces used in the Basic Substructure FDOFi Number of Free Degrees of Freedom in Substructure i Fi Fj Forces at the Ends of the Static Spring Element of Freedom Fm Vector Containing Loads Applied to Master Degrees of 1 Fml Load Vector for the Master Degrees of Freedom Substructure of Freedom of ubstructure 2 pm2 Load Vector for the Master Degrees S of Freedom of S ubstructure i Fmi Load Vector for the Master Degrees VIII FnlUm) The Condensed Generalized Governing Matrix Equation in Terms of the Master Degree of Freedom Vector JJrri Fc.