Algebraic Equations of Linear Elasticity: Novel Force-based Methods for Solid Mechanics with MATLAB®

Preface
Contents
Chapter 1: Introduction
	1.1 Background
	1.2 Differential Equations of Linear Elasticity
	1.3 Work-Energy Relations
	1.4 Algebraic Equations of Linear Elasticity
		1.4.1 Displacement Approach and the Pseudo Stiffness Matrix
		1.4.2 Second-Generation Force-Based Approach
	1.5 First-Generation Force-Based Approach
	1.6 About This Book
	References
Chapter 2: Algebraic Equations of Linear Elasticity and Their Solutions
	2.1 Overview
	2.2 Foundations of the Displacement-Based Finite Element Method
	2.3 Forces in the Principle of Virtual Work
	2.4 Forces in the Principle of Complementary Virtual Work
	2.5 The Algebraic Equations of Linear Elasticity
	2.6 Solving Statically Indeterminate Problems with MATLAB
		2.6.1 Force-Based Solutions
		2.6.2 Pseudo Stiffness Matrix
		2.6.3 Zero Flexibilities and the Pseudo Stiffness Matrix
		2.6.4 Zero Flexibilities and Rigid Body Displacements
	References
Chapter 3: Force-Based Methods in Statics
	3.1 Introduction
	3.2 Elements of a Force-Based Approach for Statics Problems
	3.3 Example Statics Problems
	3.4 Calculating Displacements
	3.5 Spatial Trusses
	References
Chapter 4: Force-Based Methods in Strength of Materials
	4.1 Introduction
	4.2 Axial Forces
		4.2.1 Governing Differential Equations
		4.2.2 A Force-Based Solution
		4.2.3 Distributed Forces and Their Discrete Force Equivalents
		4.2.4 The Force-Based Method for Axial Forces
		4.2.5 Singularity Functions
		4.2.6 Deformation-Displacement Relations
	4.3 Torsion
		4.3.1 Governing Differential Equations
		4.3.2 A Force-Based Solution
	4.4 The Pseudo Stiffness Matrix and Solving for Displacements
	4.5 The Connection to Finite Elements
Chapter 5: Force-Based Methods in Advanced Strength of Materials
	5.1 Introduction
	5.2 Beam Bending
		5.2.1 Governing Differential Eqs
		5.2.2 A Force-Based Beam Solution
		5.2.3 Distributed Forces and Their Discrete Force/Moment Equivalents
		5.2.4 The Force-Based Method for Beams
		5.2.5 A Force-Based Solution and Singularity Functions
		5.2.6 Deformation-Displacement Relations for Beams
	5.3 Solving for Displacements in Beams and the Pseudo Stiffness Matrix
	5.4 The Force-Based Method for Frames
	5.5 Force-Based Methods for Beams in Strength of Materials
	5.6 The Connection to Finite Elements
	Reference
Chapter 6: Force-Based and Displacement-Based Finite Elements
	6.1 Introduction
	6.2 Displacement-Based Finite Element Method
	6.3 Force-Based Finite Element Method
		6.3.1 Nonzero Specified Displacements in a Force-Based Method
		6.3.2 Stiffness Matrices
	6.4 Finite Element Scripts
		6.4.1 Assembly Process in Finite Elements
		6.4.2 Force-Based Finite Element Script
		6.4.3 Displacement-Based Finite Element Script
	6.5 Finite Elements in More General Cases
	References
Appendix A: MATLAB Functions
	Singularity Functions
	Equivalent Forces/Moments for Beams
Index