Advanced Finite Element Technologies

Description

The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems Front Matter....Pages i-vii Functional Analysis, Boundary Value Problems and Finite Elements....Pages 1-15 Discretization Methods for Solids Undergoing Finite Deformations....Pages 17-51 Three-Field Mixed Finite Element Methods in Elasticity....Pages 53-68 Stress-Based Finite Element Methods in Linear and Nonlinear Solid Mechanics....Pages 69-104 Tutorial on Hybridizable Discontinuous Galerkin (HDG) for Second-Order Elliptic Problems....Pages 105-129 Least-Squares Mixed Finite Element Formulations for Isotropic and Anisotropic Elasticity at Small and Large Strains....Pages 131-175 Theoretical and Numerical Elastoplasticity....Pages 177-194 On the Use of Anisotropic Triangles with Mixed Finite Elements: Application to an “Immersed” Approach for Incompressible Flow Problems....Pages 195-236