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Energy principles and variational methods in applied mechanics
Title Page; Copyright; Table of Contents; Dedication; About the Author; About the Companion Website; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Chapter 1: Introduction and Mathematical Preliminaries; 1.1 Introduction; 1.2 Vectors; 1.3 Tensors; 1.4 Summary; Problems; Chapter 2: Review of Equations of Solid Mechanics; 2.1 Introduction; 2.2 Balance of Linear and Angular Momenta; 2.3 Kinematics of Deformation; 2.4 Constitutive Equations; 2.5 Theories of Straight Beams; 2.6 Summary; Problems; Chapter 3: Work, Energy, and Variational Calculus
3.1 Concepts of Work and Energy3.2 Strain Energy and Complementary Strain Energy; 3.3 Total Potential Energy and Total Complementary Energy; 3.4 Virtual Work; 3.5 Calculus of Variations; 3.6 Summary; Problems; Chapter 4: Virtual Work and Energy Principles of Mechanics; 4.1 Introduction; 4.2 The Principle of Virtual Displacements; 4.3 The Principle of Minimum Total Potential Energy and Castigliano's Theorem I; 4.4 The Principle of Virtual Forces; 4.5 Principle of Minimum Total Complementary Potential Energy and Castigliano's Theorem II; 4.6 Clapeyron's, Betti's, and Maxwell's Theorems
4.7 SummaryProblems; Chapter 5: Dynamical Systems: Hamilton's Principle; 5.1 Introduction; 5.2 Hamilton's Principle for Discrete Systems; 5.3 Hamilton's Principle for a Continuum; 5.4 Hamilton's Principle for Constrained Systems; 5.5 Rayleigh's Method; 5.6 Summary; Problems; Chapter 6: Direct Variational Methods; 6.1 Introduction; 6.2 Concepts from Functional Analysis; 6.3 The Ritz Method; 6.4 Weighted-Residual Methods; 6.5 Summary; Problems; Chapter 7: Theory and Analysis of Plates; 7.1 Introduction; 7.2 The Classical Plate Theory; 7.3 The First-Order Shear Deformation Plate Theory
7.4 Relationships between Bending Solutions of Classical and Shear Deformation Theories7.5 Summary; Problems; Chapter 8: An Introduction to the Finite Element Method; 8.1 Introduction; 8.2 Finite Element Analysis of Straight Bars; 8.3 Finite Element Analysis of the Bernoulli-Euler Beam Theory; 8.4 Finite Element Analysis of the Timoshenko Beam Theory; 8.5 Finite Element Analysis of the Classical Plate Theory; 8.6 Finite Element Analysis of the First-Order Shear Deformation Plate Theory; 8.7 Summary; Problems; Chapter 9: Mixed Variational and Finite Element Formulations; 9.1 Introduction
9.2 Stationary Variational Principles9.3 Variational Solutions Based on Mixed Formulations; 9.4 Mixed Finite Element Models of Beams; 9.5 Mixed Finite Element Models of the Classical Plate Theory; 9.6 Summary; Problems; Chapter 10: Analysis of Functionally Graded Beams and Plates; 10.1 Introduction; 10.2 Functionally Graded Beams; 10.3 Functionally Graded Circular Plates; 10.4 A General Third-Order Plate Theory; 10.5 Navier's Solutions; 10.6 Finite Element Models; 10.7 Summary; Problems; References; Answers to Most Problems; Index; End User License Agreement
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