Kooperativer Bibliotheksverbund

UID:

Umfang: 1 online resource (482 pages)

ISBN: 3-031-08724-0

Anmerkung: Includes index. , Intro -- Preface -- About This Book -- Contents -- About the Authors -- 1 Basic Concepts of Structural Analysis -- 1.1 Types of Structures -- 1.2 Objective of Structural Analysis -- 1.3 Materials and Basic Assumptions -- 1.4 Loads -- 1.5 General Methods of Analysis -- 1.5.1 Equilibrium Conditions -- 1.5.2 Compatibility Conditions -- 1.6 Force-Displacement Relationship -- 1.7 Statical Indeterminacy -- 1.7.1 Plane Structure -- 1.7.2 Space Structures -- 1.8 Kinematic Indeterminacy -- 1.9 Two Approaches of Structural Analysis -- 2 Energy Principles -- 2.1 Introduction -- 2.2 Principle of Virtual Work -- 2.3 Principle of Complementary Virtual Work -- 2.4 Principle of Minimum Potential Energy -- 2.5 Principle of Minimum Complementary Energy -- 2.6 Castigliano's Theorems -- 2.7 Determination of Displacements -- References and Suggested Readings -- 3 Introduction to the Flexibility and Stiffness Matrix Methods -- 3.1 Introduction -- 3.2 The Flexibility Matrix Method -- 3.3 The Stiffness Method -- 3.4 Incorporation of Different Loading Conditions -- 3.5 Other Types of Loadings -- 3.5.1 Treatment by the Flexibility Matrix Method -- 3.5.2 Treatment by the Stiffness Method -- 3.6 Incorporation of Shear Deformation -- 3.7 Relation Between Flexibility and Stiffness Matrices -- 3.8 Equivalent Joint Loads -- 3.9 Choice of the Method of Analysis -- References and Suggested Readings -- 4 Direct Stiffness Method -- 4.1 Introduction -- 4.2 Local and Global Coordinate System -- 4.3 Transformation of Variables -- 4.3.1 Transformation of Member Coordinate Axes -- 4.3.2 Transformation of Member Displacement Matrix -- 4.3.3 Transformation of the Member Force Matrix -- 4.3.4 Transformation of the Member Stiffness Matrix -- 4.4 Transformation of the Stiffness Matrix of the Member of a Truss -- 4.5 Transformation of the Stiffness Matrix of the Member of a Rigid Frame. , 4.6 Transformation of the Stiffness Matrix of the Member of a Grillage -- 4.7 Transformation of the Stiffness Matrix of the Member of a Space Frame -- 4.8 Horizontally Circular Curved Beam Element -- 4.9 Overall Stiffness Matrix -- 4.10 Boundary Conditions -- 4.10.1 Boundary Conditions Corresponding to Skewed Supports -- 4.11 Computation of Internal Forces -- 4.12 Computer Program for the Truss Analysis by the Direct Stiffness Method -- 4.13 Computer Program for the Frame Analysis by Direct Stiffness Method -- 4.14 Computer Program for the Grillage Analysis by the Direct Stiffness Method -- References and Suggested Readings -- 5 Substructure Technique for the Analysis of Structural Systems -- 5.1 Introduction -- 5.2 Basic Concepts -- 5.3 Direct Stiffness Method Restated -- 5.4 The Substructure Technique -- 5.5 An Illustrative Example -- 5.6 Computer Program for the Truss Analysis by the Substructure Technique -- References and Suggested Readings -- 6 The Flexibility Matrix Method -- 6.1 Introduction -- 6.2 Element Flexibility Matrix -- 6.3 Principle of Contragredience -- 6.4 The Equilibrium Matrix -- 6.5 Construction of the Flexibility Matrix of the Structure -- 6.6 Matrix Determination of the Displacement Vector -- 6.7 Determination of Member Forces -- 6.8 Procedure of the Analysis of Statically Indeterminate Structures -- 6.9 Illustrated Examples -- 6.10 Choice of the Released Structure -- References and Suggested Readings -- 7 Elements of Elasticity -- 7.1 Introduction -- 7.2 Some Notations and Relations in the Theory of Elasticity -- 7.2.1 Surface and Body Forces -- 7.2.2 Components of Stresses -- 7.2.3 Components of Strain -- 7.2.4 Stress-Strain Relationship -- 7.3 Two-Dimensional Problems -- 7.3.1 Plane Stress -- 7.3.2 Plane Strain -- 7.3.3 Differential Equations of Equilibrium -- 7.4 Bending of Thin Plates -- 7.4.1 Basic Assumptions. , 7.4.2 Deformation of the Plate -- 7.4.3 Strain-Displacement Relationship -- 7.4.4 Stress-Strain Relationship -- 7.4.5 Equilibrium Equations -- 7.4.6 Differential Equation for Deflection -- 7.4.7 Shearing Forces -- 7.5 Boundary Conditions -- 7.5.1 Simply Supported Edge -- 7.5.2 Clamped Edge -- 7.5.3 Free Edge -- 7.5.4 Elastically Supported Edge -- 7.5.5 Edge Having Elastic Rotational Restraint -- 7.6 Concluding Remarks -- References and Suggested Readings -- 8 Introduction to the Finite Element Method -- 8.1 Introduction -- 8.2 The Finite Element Method -- 8.3 Brief History of the Development of the Finite Element Method -- 8.4 Basic Steps in the Finite Element Method for the Solution of Static Problems -- 8.5 Advantages and Disadvantages of the Finite Element Method -- References and Suggested Readings -- 9 Finite Element Analysis of Plane Elasticity Problems -- 9.1 Introduction -- 9.2 Three-Noded Triangular Element -- 9.2.1 Displacement Function -- 9.2.2 Displacement Function Expressed in Terms of Nodal Displacements -- 9.2.3 Strain-Nodal Parameter Relationship -- 9.2.4 Stress-Strain Relationship -- 9.2.5 Derivation of the Element Stiffness Matrix -- 9.2.6 Determination of Element Stresses -- 9.3 Criteria for the Choice of the Displacement Function -- 9.4 Polynomial Displacement Functions -- 9.5 Verification of the Convergence Criteria of the Displacement Function of 3-Noded Triangular Element -- 9.6 Number of Terms in a Polynomial -- 9.7 Four-Noded Rectangular Element -- 9.7.1 Displacement Function -- 9.7.2 Displacement Function in Terms of Nodal Displacements -- 9.7.3 Strain-Nodal Displacement Relationship -- 9.7.4 Stress-Strain Relationship -- 9.7.5 Derivation of the Element Stiffness Matrix -- 9.7.6 Evaluation of Element Stresses -- 9.8 A Note on the Rectangular Element -- 9.9 A Note on Element Stresses. , 9.10 Computer Program for the Plane Stress Analysis Using Three-Noded Triangular Element -- Bibliography -- 10 Isoparametric and Other Element Representations and Numerical Integrations -- 10.1 Introduction -- 10.2 Shape Function or Interpolation Function -- 10.3 Determination of Shape Functions -- 10.3.1 Linear 2-D Element -- 10.3.2 Quadratic 2-D Element -- 10.4 Plane Stress Isoparametric Linear Element -- 10.4.1 Displacement Function in Terms of Nodal Parameters -- 10.4.2 Strain-Nodal Parameter Relationship -- 10.4.3 Evaluation of [B] Matrix -- 10.4.4 Element Stiffness Matrix -- 10.4.5 Convergence of Isoparametric Elements -- 10.4.6 Concept of Isoparametric Element -- 10.5 Numerical Integration -- 10.5.1 Gaussian Quadrature Formula -- 10.5.2 Gaussian Integration of Two Variables -- 10.6 Lagrangian Interpolation -- 10.7 Natural Coordinates and Higher Order Triangular Elements -- 10.7.1 One-Dimensional Element -- 10.7.2 Higher Order Triangular Elements -- 10.8 The Quadratic Triangle for the Plane Stress Problem -- 10.9 Numerical Integration of Area Coordinates -- 10.10 Triangular Isoparametric Elements for the Analysis of Plane Stress Problems -- 10.11 Allman's Triangular Plane Stress Element -- 10.12 Computer Program for the Solution of Plane Stress Problem Using Isoparametric Element -- References and Suggested Readings -- 11 Finite Element Analysis of Plate Bending Problems -- 11.1 Introduction -- 11.2 Beam Element -- 11.2.1 Displacement Function -- 11.2.2 Displacement Function in Terms of Nodal Displacements -- 11.2.3 Strain (Curvature)-Nodal Parameter Relationship -- 11.2.4 Stress (Moment)-Strain (Curvature) Relationship -- 11.2.5 Derivation of the Element Stiffness Matrix -- 11.2.6 Determination of Equivalent Loading on the Beam -- 11.3 Rectangular Plate Bending Element -- 11.3.1 Displacement Function. , 11.3.2 Displacement Function Expressed in Terms of Nodal Displacements -- 11.3.3 Strain-Nodal Parameter Relationship -- 11.3.4 Stress (Moment)-Strain (Curvature) Relationship -- 11.3.5 Derivation of the Element Stiffness Matrix -- 11.4 Parallelogram Element of Plate Bending -- 11.4.1 Displacement Function -- 11.4.2 Displacement Function in Terms of Nodal Displacements -- 11.4.3 Curvature-Nodal Parameter Relationship -- 11.4.4 Moment-Curvature Relationship -- 11.4.5 Element Stiffness Matrix -- 11.5 Hermitian Polynomial Interpolation -- 11.6 A Conforming Plate Bending Element -- 11.7 Isoparametric Plate Bending Element -- 11.7.1 Displacement Function -- 11.7.2 Strain-Nodal Displacement Relationship -- 11.7.3 Stress-Strain Relationship -- 11.7.4 Element Stiffness Matrix -- 11.7.5 Reduced Integration Technique -- 11.8 Smoothed Stresses -- 11.9 Triangular Plate Bending Elements -- 11.10 DKT Element -- 11.10.1 Constraint Equations -- 11.10.2 Transformation Matrix -- 11.10.3 Element Stiffness Matrix -- 11.11 The Patch Test -- 11.11.1 The Patch Test for the Plane Stress Element -- 11.11.2 The Patch Test for Plate Bending Elements -- 11.12 Horizontally Curved Isoparametric Beam -- 11.12.1 Displacement Function in Terms of Nodal Parameters -- 11.12.2 Stress-Strain Relations -- 11.12.3 Strain-Displacement Relationship -- 11.12.4 Element Stiffness Matrix -- 11.13 Nonuniform Straight Beam Element -- 11.14 Computer Program for Isoparametric Quadratic Bending Element -- References and Suggested Readings -- 12 Finite Element Analysis of Shells -- 12.1 Introduction -- 12.2 Flat Shell Element -- 12.2.1 Transformation of the Stiffness Matrix and Assembly -- 12.3 Shell of Revolution -- 12.4 General Shell Finite Element of Triangular Shape -- 12.4.1 Derivation of the Stiffness Matrix -- 12.4.2 Consistent Load Vector -- 12.4.3 Condensation of Stiffness Matrix. , 12.5 Isoparametric General Shell Element.

Weitere Ausg.: Print version: Mukhopadhyay, Madhujit Matrix and Finite Element Analyses of Structures Cham : Springer International Publishing AG,c2023 ISBN 9783031087233

Sprache: Englisch