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Computational methods in nonlinear structural and solid mechanics
papers presented at the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics, held 6-8 October 1980, Washington, D.C
Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics (1980 : Washington, D.C.)
1 online resource (vi, 465 pages) : illustrations
Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers com.
Front Cover; Computational Methods in Nonlinear Structural and Solid Mechanics; Copyright Page; Table of Contents; PREFACE; Part 1: Nonlinear Mathematical Theories and Formulation Aspects; CHAPTER 1.A NONLINEAR THEORY OF GENERAL THIN-WALLED BEAMS; Abstract; 1. INTRODUCTION; 2. THEORETICAL DEVELOPMENT; 3. FINITE-DIFFERENCE FORMULATION; 4. COMPARISON WITH EXPERIMENT OR INDEPENDENT PREDICTIONS; 5. SUMMARY OF CURRENT RESULTS; 6. CONCLUSIONS AND COMMENTS; REFERENCES; CHAPTER 2. STABILITY ANALYSIS OF STRUCTURES VIA A NEW COMPLEMENTARY ENERGY METHOD; Abstract; INTRODUCTION.
1. PRELIMINARIES AND A GENERAL VARIATIONAL PRINCIPLE2. FINITE DEFORMATIONS OF A BEAM; CLOSURE; REFERENCES; CHAPTER 3.A LARGE DEFORMATION FORMULATION FOR SHELL ANALYSIS BY THE FINITE ELEMENT METHOD; Abstract; INTRODUCTION; STRATEGIES OF SHELL ELEMENT DERIVATION; FORMULATION OF LARGE DEFORMATION SHELL ELEMENT; 3D CONTINUUM ELEMENT SHELL ELEMENT; NUMERICAL EXAMPLES; CONCLUSIONS; REFERENCES; APPENDIX; Part 2: Computational Strategies for Nonlinear Programs; CHAPTER 4. RECENT ADVANCES IN REDUCTION METHODS FOR NONLINEAR PROBLEMS; Abstract; NOMENCLATURE; 1. INTRODUCTION.
2. REDUCTION METHODS FOR NONLINEAR STATIC PROBLEMS3. COMPUTATIONAL PROCEDURE USED WITH REDUCTION METHODS; 4. CASE OF PRESCRIBED EDGE DISPLACEMENTS; 5. USE OF REDUCED-BASIS TECHNIQUE IN CONJUNCTION WITH MIXED FINITE ELEMENT MODELS; 6. REDUCTION METHODS FOR NONLINEAR DYNAMIC PROBLEMS; 7. TWO-STAGE RAYLEIGH-RITZ AND BUBNOV-GALERKIN TECHNIQUES; 8. NUMERICAL STUDIES; 9. FUTURE DIRECTIONS FOR RESEARCH ON REDUCTION METHODS; 10. CONCLUDING REMARKS; REFERENCES; CHAPTER 5. ADAPTIVE LOAD IN CREMENTATION INELASTIC-PLASTIC FINITE ELEMENT ANALYSIS; Abstract; INTRODUCTION.
INCREMENTAL SECANT STIFFNESS FORMULATIONCONTROLLING LOAD PATH DISCRETIZATION ERROR; ADAPTIVE SOLUTION ALGORTIHM; EXAMPLE ANALYSES USING ADAPTIVE INCREMENTATION; CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS; REFERENCES; CHAPTER 6.A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES SNAP-THROUGH -- Abstract; INTRODUCTION; RIKS METHOD; A MODIFIED RIKS METHOD; AN ACCELERATED MODIFIED NEWTON-RAPHSON METHOD WITH FIXED LENGTH INCREMENTS; APPLICATIONS; CONCLUSIONS; REFERENCES.
CHAPTER 7. AN EFFICIENT AND ACCURATE ITERATIVE METHOD, ALLOWING LARGE INCREMENTAL STEPS, TO SOLVE ELASTO-PLASTIC PROBLEMSAbstract; 1. INTRODUCTION; 2. SYSTEM OF EQUATIONS TO SOLVE; 3. REQUIRED PROPERTIES OF AN EFFICIENT SOLUTION METHOD; 4. STATE DETERMINATION ALGORITHM; 5. IMPROVEMENTS OF THE NEWTON-RAPHSON METHOD FOR ELASTO-PLASTIC CASES; 6. EXAMPLES; 7. CONCLUSIONS; REFERENCES; CHAPTER 8.COMPUTATIONAL STRATEGIES FOR THE SOLUTION OF LARGE NONLINEAR PROBLEMS VIA QUASI-NEWTON METHODS; Abstract; 2. NEWTON METHODS; 3. QUASI-NEWTON METHODS; 4. COMPUTATIONAL IMPLEMENTATION OF QUASI-NEWTON UPDATES.
editors, Ahmed K. Noor and Harvey G. McComb, Jr.
Sponsored by George Washington University and other organizations.
"Published as a special issue of the journal Computers & structures, volume 13, number 1/2."
Computers and structures ; vol. 13 no 1/2