Novel Finite Element Technologies for Solids and Structures

✍ Scribed by Jörg Schröder, Paulo de Mattos Pimenta

• Publisher: Springer International Publishing
• Year: 2020
• Tongue: English
• Leaves: 202
• Series: CISM International Centre for Mechanical Sciences 597
• Edition: 1st ed. 2020
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-vii
Engineering Notes on Concepts of the Finite Element Method for Elliptic Problems (Jörg Schröder)....Pages 1-39
Sensitivity Analysis Based Automation of Computational Problems (Jože Korelc, Teja Melink)....Pages 41-67
Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity (Fleurianne Bertrand, Bernhard Kober, Marcel Moldenhauer, Gerhard Starke)....Pages 69-106
A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity (Nils Viebahn, Jörg Schröder, Peter Wriggers)....Pages 107-126
A Fully Nonlinear Beam Model of Bernoulli–Euler Type (Paulo de Mattos Pimenta, Sascha Maassen, Cátia da Costa e Silva, Jörg Schröder)....Pages 127-151
Isogeometric Analysis of Solids in Boundary Representation (Sven Klinkel, Margarita Chasapi)....Pages 153-197

✦ Subjects

Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical and Applied Mechanics