Mixed Finite Element Technologies
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Mixed Finite Element Technologies
Author: Peter Wriggers
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-06-16
Mixed finite element methods are a tool to solve complex engineering problems of different nature. This subject is treated in the volume from the engineering and the mathematical point. Different applications are considered which depict the value of mixed formulations in engineering on one side. On the other side the mathematical background is provided including proofs of convergence and stability of these methods and adequate solvers for mixed problems are discussed. This broad spectrum yields an indepth treatment of mixed methods from different perspectives.
Advanced Finite Element Technologies
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.
Novel Finite Element Technologies for Solids and Structures
This book presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics.