Kooperativer Bibliotheksverbund

UID:

Format: XXI, 473 p. 289 illus., 1 illus. in color. , online resource.

Edition: 1st ed. 2022.

ISBN: 9783031087240

Content: This textbook has been primarily written for undergraduate and postgraduate engineering students studying the mechanics of solids and structural systems. The content focuses on matrix, finite elements, structural analysis, and computer implementation in a unified and integrated manner. Using classical methods of structural analysis, it discusses matrix and the finite element methods in an easy-to-understand manner. It consists of a large number of diagrams and illustrations for easy understanding of the concepts. All the computer codes are presented in "FORTRAN" AND "C". This textbook is highly useful for the undergraduate and postgraduate engineering students. It also acquaints the practicing engineers about the computer-based techniques used in structural analysis.

Note: Basic Concepts of Structural Analysis -- Energy Principles -- Introduction To The Flexibility and Stiffness Matrix Methods -- Direct Stiffness Method -- Substructure Technique for the Analysis of Structural Systems -- The Flexibility Matrix Method -- Elements of Elasticity -- Introduction to The Finite Element Method -- Finite Element Analysis of Plane Elasticity Problems -- Isoparametric and Other Element Representations and Numerical Integrations -- Finite Element Analysis of Plate Bending Problems -- Finite Element Analysis of Shells -- Semi-Analytical and Spline Finite Strip Method of Analyses of Plate Bending -- Dynamic and Instability Analyses By The Finite Element Method -- The Finite Difference Method For The Analysis Of Beams And Plates -- Adaptive Finite Element Analysis -- Geometrical Non-Linear Finite Element Analysis -- Finite Element Method Of Analysis Of Stiffened Plates -- Selected Topics.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031087233

Additional Edition: Printed edition: ISBN 9783031087257

Additional Edition: Printed edition: ISBN 9783031087264

Language: English

DOI: 10.1007/978-3-031-08724-0

URL: https://doi.org/10.1007/978-3-031-08724-0

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

URL: Cover

UID:

Format: 1 online resource (482 pages)

ISBN: 3-031-08724-0

Note: 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.

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

Language: English