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  3. Non-linear Modeling and Analysis of Solids and Structures
  • Cited by 79
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2009
Online ISBN:
9780511812163
DOI:
https://doi.org/10.1017/CBO9780511812163
Subjects:
Mathematics, Engineering, Fluid Dynamics and Solid Mechanics, Solid Mechanics and Materials
Information

Book description

This book presents a theoretical treatment of nonlinear behaviour 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 summarises recent results on momentum and energy conserving integration of time-dependent problems. Exercises, examples and algorithms are included throughout.

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