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.
Mục lục
Notes on Basic Concepts of the Finite Element Method for Elliptic Problems.- Sensitivity Analysis Based Automation of Computational Problems.- Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity.- A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity.- Simple Equilibrium Finite Elements for Geometrically Exact Bernoulli-Euler Beams and Kirchhoff-Love Shells.- Isogeometric Analysis of Solids in Boundary Representation.
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