Matrix Structural Analysis and the Finite Element Methods Using Scilab and Octave. A Problem-Solving Approach

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgments
List of Figures
List of Tables
Section I MATRIX STRUCTURAL ANALYSIS
	1 Introduction
		1.1 Structural Classification
			1.1.1 Plane Truss
			1.1.2 Beam
			1.1.3 Plane Frame
			1.1.4 Grid
			1.1.5 Space Truss
			1.1.6 Space Frame
		1.2 Static/Kinematic Indeterminacy
		1.3 Matrix Structural Analysis
			1.3.1 The Flexibility Coefficient
			1.3.2 The Stiffness Coefficients
			1.3.3 Flexibility and Stiffness Matrices
		1.4 Scilab Software Environment
		1.5 Octave Software Environment
		1.6 Programming in Scilab and Octave
			1.6.1 Operators and Their Precedence
			1.6.2 Variables
			1.6.3 Data Types
			1.6.4 Expressions and Statements
			1.6.5 If/Else Statement
			1.6.6 While Statement
			1.6.7 For Statement
			1.6.8 Branching/Case Statements
			1.6.9 User-Defined Functions
			1.6.10 Simple File Input/Output
		1.7 Problems
	2 The Basic Methods
		2.1 The Basic Flexibility Method
			2.1.1 Solution Steps
			2.1.2 Examples
		2.2 The Basic Stiffness Method
			2.2.1 Solution Steps
			2.2.2 Examples
		2.3 Problems
	3 The Formalized Methods
		3.1 The Formalized Flexibility Method
			3.1.1 Member Flexibility
			3.1.2 Derivation of Structure Flexibility
			3.1.3 Solving for AQ and Solution Steps
			3.1.4 Examples
		3.2 The Formalized Stiffness Method
			3.2.1 Member Stiffness
			3.2.2 Derivation of Structure Stiffness
			3.2.3 Assembling Structure Stiffness
			3.2.4 Solving for DJ and Solution Steps
			3.2.5 Examples
		3.3 Problems
	4 The Direct Stiffness Method
		4.1 Introduction
		4.2 Complete Member Stiffness
			4.2.1 Spring and Bar Elements
			4.2.2 Beam
			4.2.3 Plane Truss
			4.2.4 Plane Frame
			4.4.5 Grid Structure
			4.2.6 Space Truss
			4.2.7 Space Frame
		4.3 Solution Steps in the Direct Stiffness Method
		4.4 Examples
		4.5 Problems
	5 Special Cases in the Direct Stiffness Method
		5.1 Introduction
		5.2 Different Element Types in a Structure
		5.3 Beam on Elastic Foundation
			5.3.1 Two-parameters Mechanical Model
		5.4 Non-Prismatic Members
		5.5 Inclined Roller support
		5.6 Member Discontinuities (Hinge/Roller)
		5.7 Symmetric and Anti-symmetric Structures
		5.8 Examples
		5.9 Problems
Section II FINITE ELEMENT METHODS
	6 Introduction and 1D Finite Element Analysis
		6.1 Introduction
			6.1.1 Nodes and Finite Elements
			6.1.2 A Brief History
			6.1.3 An Overview
		6.2 3D Elasticity
		6.3 Interpolation/Shape Function
		6.4 Element Stiffness Matrix
			6.4.1 Equivalent Nodal Loads Vector
		6.5 Common Steps in the FEM
		6.6 Symbolic Computation
		6.7 1D FE Analysis
			6.7.1 Stiffness of a Linear Bar Element
			6.7.2 Stiffness of a Quadratic Bar Element
			6.7.3 Beam Elements
			6.7.4 DSM as a Special Case of the FEM
		6.8 Problems
	7 2D Finite Element Analysis
		7.1 Introduction
		7.2 Plane Stress, Plane Strain and Axisymmetric Problems
		7.3 Constant Strain Triangle
			7.3.1 Stiffness Matrix of a CST
		7.4 Linear Strain Triangle
		7.5 Bi-linear Rectangular Element
		7.6 Natural Coordinate & Isoparametric Representation
			7.6.1 Relationship between Global and NaturalCoordinates
		7.7 Iso-P Representation for Quadrilateral Elements
			7.7.1 Derivative Relationships in 2D
		7.8 Numerical Integration Using Gauss Quadrature
		7.9 Axisymmetric Problem
		7.10 Problems
	8 3D Finite Element Analysis
		8.1 Introduction
		8.2 Tertahedral Element
			8.2.1 Stiffness Matrix of a Tetrahedral Element
		8.3 Hexahedral Element
			8.3.1 Stiffness Matrix of a Hexahedral Element
		8.4 Problems
	Beam Deflection
	Fixed-End Actions
	FPS vs SI Unit Conversion
	References
	Index