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9780898712308 Academic Inspection Copy

Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics

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A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator splitting methods such as alternating methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator splitting methods (coupled to finite element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods traditionally used to study them. These ideas are then applied to specific classes of mechanical problems.
Chapter 1: Some Continuous Media and Their Mathematical Modeling Chapter 2: Variational Formulations of the Mechanical Problems Chapter 3: Augmented Lagrangian Methods for the Solution of Variational Problems Chapter 4: Viscoplasticity and Elastoviscoplasticity in Small Strains Chapter 5: Limit Load Analysis Chapter 6: Two Dimensional Flow of Incompressible Viscoplastic Fluids Chapter 7: Finite Elasticity Chapter 8: Large Displacement Calculations of Flexible Rods References Index.
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