NASA Contractor Report 198502 Concurrent Probabilistic Simulation of High Temperature Composite Structural Response Frank Abdi Alpha STAR Research Corporation Los Angeles, California July 1996 Prepared for Lewis Research Center Under Contract NAS3-26997 National Aeronautics and Space Administration ASC-95-1001 Acknowledgement This report was prepared under NASA Small Business Innovative Research Program (SBIR) Phase II (Contract No. NAS3-26997) funding. Dr. F. Abdi is the Alpha STAR program manager. Other member of the team include Mr. B. Littlefield, Mr. B Golod, Dr. J. Yang, Dr. J. Hadian, Mr. Y. Mirvis, and Mr. B. Lajevardi. We also would like to acknowledge special contribution by NASA program manager Dr. C. C. Chamis, and Dr. P. L.N. Murthy for useful discussion and suggestions for improvement. We acknowledge the invaluable contribution of Mr. D. Collins and Dr. B. Nour-Omid. Our special thanks to Mr. R. Lorenz whose help was invaluable in putting the report together. ASC-95-1001 Contents Section Page 1.0 INTRODUCTION ................................................................................................... 1-1 1.1 Background .................................................................................................... 1-2 1.1.1 Hardware For Parallel Processing ..................................................... 1-4 1.1.2 Parallel Sparse Solvers .................................................................... 1-6 1.13 Probabilistic Simulation ................................................................... 1-8 1.2 GENOA Software Overview ........................................................................ 1-10 1.3 Product Strategy .......................................................................................... 1-12 1.4 Product Brochure .......................................................................................... 1-16 1.5 References .................................................................................................... 1-24 2.0 OBJECTIVES AND SCOPE ....................................................................................... 2-1 3.0 GENOA: AN INTEGRATED SOFTWARE PACKAGE .............................................. 3-1 3.1 Module 1: Executive Controller System (ECS) ................................................. 3-4 3.2 Module 2: User Interface And Commercial Packaging of GENOA ..................... 3-6 3.3 Domain Decomposition Parallelization Routines ............................................ 3-7 3.3.1 Module 3: Recursive Inertial Partitioning (RIP) ................................ 3-7 3.3.2 Module 4: Dynamic Loads Balancing MAESTRO ............................. 3-11 3.3.2.1 Testing Facility Usage (TFU) ............................................ 3-12 3.3.2.2 Message Passing Paradigm ................................................ 3-12 3.3.2.3 Task Allocation Table (TAT) ............................................. 3-13 3.3.2.4 Multi Factor Optimization ................................................ 3-13 3.3.3 Module 5: Alpha Star Multifrontal (AMF) Algorithm .................... 3-15 3.4 Structural Analysis Methods for Metal Matrix Composites ............................ 3-18 3.4.1 HITCAN: A source for baseline Analytical Capabilities ................. 3-18 3.4.2 NESSUS: 3D Inelastic Finite Element Analysis .............................. 3-20 3.4.3 METCAN: Bridging the Micro-to-Macro Gap .................................. 3-21 3.4.4 CEMCAN Integration ..................................................................... 3-26 3.4.5 ICAN Integration ........................................................................... 3-28 3.4.6 Constitutive Relationship For Probabilistic Composite Micromechanics .............................................................................. 3-28 II ASC-95-1001 Contents Section ................................................................................................ Page 4.0 EXECUTIVE CONTROLLER AND GRAPHICAL USER INTERFACE ....................... 4-1 4.1 Automatic File Naming System ...................................................................... 4-1 4.2 Project Directory ............................................................................................ 4-2 4.2.1 Project Directory Usage ..................................................................... 4-2 4.3 History .......................................................................................................... 4-2 4.4 Job Linking ..................................................................................................... 4-5 4.5 Graphical User Interface ................................................................................ 4-6 5.0 PARTITIONING FINITE ELEMENT MESH FOR CONCURRENT COMPUTING ...... 5-1 5.1 Mesh Partitioning .......................................................................................... 5-1 5.2 RIP and PEEL Algorithm ................................................................................ 5-1 5.3 Forced Partitioning ........................................................................................ 5-6 5.4 Reference ....................................................................................................... 5-9 6.0 PARALLEL STRUCTURAL ANALYSIS METHODS ................................................. 6-1 6.1 Problem Scaling By Exploiting Multi-Level Parallelism ................................. 6-1 6.2 Module 5: Alpha Star Multi-Frontal (AFM) Algorithm .................................. 6-4 6.2.1 Matrix Assembly .............................................................................. 6-4 6.2.2 Triangular Decomposition ................................................................. 6-5 6.2.3 Climb Operation .............................................................................. 6-7 6.2.4 Triangular Solvers ............................................................................ 6-8 6.3 Message Passing System in GENOA .............................................................. 6-13 6.3.1 Messages and Routing in PVM ......................................................... 6-13 6.4 MAESTRO: Dynamic Load Balancing ........................................................... 6-15 6.4.1 Domain Decomposer ....................................................................... 6-15 6.4.2 Alpha Star Multifrontal Algorithm (AMF) .................................... 6-18 6.4.3 Supervisor ...................................................................................... 6-19 6.4.4 Parallel Virtual Machine ............................................................... 6-20 6.4.5 Multifactor Optimization ............................................................... 6-20 6.5 References .................................................................................................... 6-25 III ASC-95-1001 Contents Section ................................. • ...-..---...--.-.---....--............. •................• .. .. Pa ge 7.0 STOCHASTIC STRUCTURAL ANALYSIS METHODS FOR COMPOSITES .............. 7-1 7.1 An Integrated Modularized Constituent Material Strength and Risk Assessment Analysis ........................................................................................................ 7-1 7.1.1 PROMISS Integrated With METCAN ............................................... 7-2 7.1.2 PROMISS Integrated With ICAN ..................................................... 7-2 7.1.3 PROMISS Integrated With CEMCAN ............................................... 7-4 7.1.4 Integrated of PROMISS With HITCAN ............................................ 7-5 7.1.5 Micromechanical Risk Assessment .................................................. 7-11 7.1.6 Integration of Environmental and Test Data With A Stochastic Simulation ..................................................................................... 7-12 7.2 References .................................................................................................... 7-13 8.0 VERIFICATION AND DEMONSTRATION ............................................................. 8-1 8.1 Numerical Results of Parallel Analysis ............................................................... 8.2 METCAN and PROMISS Results ..................................................................... 8-1 8.2.1 Composite Cantilever Beam Analysis ............................................... 8-8 8.3 Validation of AMF and NESSUS Sequential Solver ..................................... 8-13 8.3.1 Demonstration Problem No. 1 .......................................................... 8-13 8.3.2 Demonstration Problem No. 2 .......................................................... 8-14 8.3.3 Demonstration Problem No. 3 .......................................................... 8-15 8.3.4 Demonstration Problem No. 4 ........................................................... 8-17 8.4 References .................................................................................................... 8-19 9.0 SUMMARY AND CONCLUSION ........................................................................... 9-1 IV ASC-95-1001 Illustrations Figure .................................................................................................. Page 1-1 Speedup Given by Amdahl's Law .................................................................................. 1-3 1-2 Speedup Given by Problem Scaling ................................................................................. 1-4 1-3 Three Multiprocessor