Synopses & Reviews
This book presents a theoretical treatment of nonlinear behavior of solids and structures in such a way that it is suitable for numerical computation, typically using the Finite Element Method. Starting out from elementary concepts, the author systematically uses the principle of virtual work, initially illustrated by truss structures, to give a self-contained and rigorous account of the basic methods. The author illustrates the combination of translations and rotations by finite deformation beam theories in absolute and co-rotation format, and describes the deformation of a three-dimensional continuum in material form. A concise introduction to finite elasticity is followed by an extension to elasto-plastic materials via internal variables and the maximum dissipation principle. Finally, the author presents numerical techniques for solution of the nonlinear global equations and summarizes recent results on momentum and energy conserving integration of time-dependent problems. Exercises, examples and algorithms are included throughout.
Numerical analysis and, in particular, the Finite Element method is now a regular part of experimental analysis. Steen Krenk emphasizes the formulation of appropriate models for solids and structures in the non-linear regime. Based on successful graduate courses, the book comes with accompanying finite element Matlab code, making it a valuable theoretical and practical text for applied mathematicians and mechanical engineers.
Numerical analysis and in particular, the finite-element method, is now a regular part of experimental analysis. This book emphasises the formulation of appropriate models for solids and structures in the non-linear regime. Accompanied by finite-element Matlab files, this is a valuable theoretical and practical text for applied mathematicians and mechanical-engineers.
Finite element analysis for non-linear solids and structure porblems. Graduate level with Matlab code.
Table of Contents
1. Introduction; 2. Non-linear bar elements; 3. Finite rotations; 4. Finite rotation beam theory; 5. Co-rotating beam elements; 6. Co-rotating shell elements; 7. Non-linear deformation of solids; 8. Elasto-plastic solids; 9. Classical plasticity algorithms; 10. Dilating and softening materials; 11. Numerical solution techniques; 12. Dynamic effects and algorithms;