Variational, Incremental and Energy Methods in Solid Mechanics and Shell Theory, Volume 4

1st Edition

Authors: J. Mason
Hardcover ISBN: 9780444418999
eBook ISBN: 9781483289649
Imprint: North Holland
Published Date: 1st January 1980
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Table of Contents



Chapter 1. Mathematical Preliminaries

1.1 Tensor Formulas in Three-Dimensional Euclidean Spaces

1.2 Tensor Fomulas For Surfaces

1.3 Basic Concepts and Definitions in the Theory of Abstract Spaces and Operators

1.4 Fundamentals of the Classical Calculus of Variations

1.5 Differentials and Derivatives of Operators — Variations

1.6 Variational Boundary Value Problems

1.7 Variational Methods of Approximation

Part I — Three-Dimensional Theory

Chapter 2. Kinematics and Stress in Three-Dimensional Solid Continua

2.1 Description of Motion, Coordinates, Reference and Deformed States

2.2 Kinematics of Deformation

2.3 Kinematics of Incremental Deformation

2.4 Definitions of Stress — Stress Rates

2.5 Incremental Stresses

2.6 External Loadings — Boundary Conditions

2.7 Illustrative Example of Physical Components of Displacements and Stress

Chapter 3. General Principles - The First and the Second Laws of Thermodynamics

3.1 Kinematics of Rigid Body Motions — Invariance Requirements

3.2 the First Law of Thermodynamics

3.3 the Second Law of Thermodynamics

3.4 the Principles of Virtual Displacements and Virtual Forces

3.5 Equations of Equilibrium in Physical Components For Cylindrical and Spherical Coordinates

Chapter 4. Constitutive Material Laws

4.1 Elastic, Hypoelastic and Hyperelastic Materials

4.2 Elastic-Plastic Materials

4.3 Visco-Elastic Materials

Part II - Shell Theory

Chapter 5. Deformation and Stress in Shells

5.1 Shell Midd


Studies in Applied Mechanics, 4: Variational, Incremental, and Energy Methods in Solid Mechanics and Shell Theory covers the subject of variational, incremental, and energy methods in Solid Mechanics and Shell Theory from a general standpoint, employing general coordinates and tensor notations.

The publication first ponders on mathematical preliminaries, kinematics and stress in three-dimensional solid continua, and the first and second laws of thermodynamics. Discussions focus on the principles of virtual displacements and virtual forces, kinematics of rigid body motions, incremental stresses, kinematics of incremental deformation, description of motion, coordinates, reference and deformed states, tensor formulas for surfaces, and differentials and derivatives of operators. The text then elaborates on constitutive material laws, deformation and stress in shells, first law of thermodynamics applied to shells, and constitutive relations and material laws for shells. Concerns cover hyperelastic incremental material relations, material laws for thin elastic shells, incremental theory and stability, reduced and local forms of the first law of thermodynamics, and description of deformation and motion in shells. The book examines elastic stability, finite element models, variational and incremental principles, variational principles of elasticity and shell theory, and constitutive relations and material laws for shells.

The publication is a valuable reference for researchers interested in the variational, incremental, and energy methods in solid mechanics and shell theory.


© North Holland 1980
North Holland
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@qu:This book is a significant contribution to the field of solid mechanics, especially to shell theory. It serves as an excellent textbook, and as a reference... Mathematical rigor, and comprehensive examples make this book a valuable tool for research and education. @source:Mathematics Abstracts

About the Authors

J. Mason Author