Equilibrium Finite Element Formulations

J. P. Moitinho de Almeida, Edward A. Maunder

• Publisher: Wiley
• Year: 2016
• Print ISBN: 9781118424155
• eBook ISBN: 9781118926208
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

A comprehensive treatment of the theory and practice of equilibrium finite element analysis in the context of solid and structural mechanics

Equilibrium Finite Element Formulations is an up to date exposition on hybrid equilibrium finite elements, which are based on the direct approximation of the stress fields. The focus is on their derivation and on the advantages that strong forms of equilibrium can have, either when used independently or together with the more conventional displacement based elements. These elements solve two important problems of concern to computational structural mechanics: a rational basis for error estimation, which leads to bounds on quantities of interest that are vital for verification of the output and provision of outputs immediately useful to the engineer for structural design and assessment.

Key features:

• Unique in its coverage of equilibrium – an essential reference work for those seeking solutions that are strongly equilibrated. The approach is not widely known, and should be of benefit to structural design and assessment.
• Thorough explanations of the formulations for: 2D and 3D continua, thick and thin bending of plates and potential problems; covering mainly linear aspects of behaviour, but also with some excursions into non-linearity.
• Highly relevant to the verification of numerical solutions, the basis for obtaining bounds of the errors is explained in detail.
• Simple illustrative examples are given, together with their physical interpretations.
• The most relevant issues regarding the computational implementation of this approach are presented.

When strong equilibrium and finite elements are to be combined, the book is a must-have reference for postgraduate students, researchers in software development or numerical analysis, and industrial practitioners who want to keep up to date with progress in simulation tools.

Table of contents

• Cover
• Title Page
• Copyright
• Table of Contents
• Dedication
• Preface
• List of Symbols
• Chapter 1: Introduction
• Chapter 2: Basic Concepts Illustrated by Simple Examples
• Chapter 3: Equilibrium in Other Finite Element Formulations
• Chapter 4: Formulation of Hybrid Equilibrium Elements
• Chapter 5: Analysis of the Kinematic Stability of Hybrid Equilibrium Elements
• Chapter 6: Practical Aspects of the Kinematic Stability of Hybrid Equilibrium Elements
• Chapter 7: A Variational Basis of the Hybrid Equilibrium Formulation
• Chapter 8: Recovery of Complementary Solutions
• Chapter 9: Dual Analyses for Error Estimation & Adaptivity
• Chapter 10: Dynamic Analyses
• Chapter 11: Non-Linear Analyses
• A: Fundamental Equations of Structural Mechanics
• B: Computer Programs for Equilibrium Finite Element Formulations
• Subject Index
• End User License Agreement