Balas / Bala? / Sládek Stress Analysis by Boundary Element Methods

1. Auflage 2013
ISBN: 978-1-4832-9174-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 23, 699 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

The boundary element method is an extremely versatile and powerful tool of computational mechanics which has already become a popular alternative to the well established finite element method. This book presents a comprehensive and up-to-date treatise on the boundary element method (BEM) in its applications to various fields of continuum mechanics such as: elastostatics, elastodynamics, thermoelasticity, micropolar elasticity, elastoplasticity, viscoelasticity, theory of plates and stress analysis by hybrid methods. The fundamental solution of governing differential equations, integral representations of the displacement and temperature fields, regularized integral representations of the stress field and heat flux, boundary integral equations and boundary integro-differential equations are derived. Besides the mathematical foundations of the boundary integral method, the book deals with practical applications of this method. Most of the applications concentrate mainly on the computational problems of fracture mechanics. The method has been found to be very efficient in stress-intensity factor computations. Also included are developments made by the authors in the boundary integral formulation of thermoelasticity, micropolar elasticity, viscoelasticity, plate theory, hybrid method in elasticity and solution of crack problems. The solution of boundary-value problems of thermoelasticity and micropolar thermoelasticity is formulated for the first time as the solution of pure boundary problems. A new unified formulation of general crack problems is presented by integro-differential equations.

Autoren/Hrsg.

Balas, J.

Bala?, J.

Sládek, J.

Sládek, V.

Inhaltsverzeichnis

1;Front Cover;1
2;Stress Analysis by Boundary Element Methods;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;6
6;Basic Symbols;12
7;Chapter 1. SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY THE BOUNDARY INTEGRAL EQUATION METHOD (BIEM);14
7.1;1.1 Introduction;14
7.2;1.2 Ordinary Differential Equations;17
7.3;1.3 Partial Differential Equations;19
8;Chapter 2. ELASTOSTATICS;24
8.1;2.1 Introduction;24
8.2;2.2 Governing Equations and Fundamental Solutions;25
8.3;2.3 The Somigliana Identity. Boundary Integral Equations (BIE);39
8.4;2.4 Integral Representation of Stresses. Boundary Integro-Differential Equations (BIDE);51
8.5;2.5 Stresses on the Boundary;60
8.6;2.6 BIE and BIDE for an Anisotropic Medium;63
8.7;2.7 Axisymmetric Problems;65
8.8;2.8 Semi-Infinite Problems;85
8.9;2.9 Numerical Implementation;98
8.10;2.10 Numerical Examples;148
9;Chapter 3. ELASTODYNAMICS;214
9.1;3.1 Introduction;214
9.2;3.2 Equations of Motion;216
9.3;3.3 Fundamental Solutions;220
9.4;3.4 Integral Representations of Displacements and Stresses;224
9.5;3.5 Boundary Integral and Integro-Differential Equations;230
9.6;3.6 Numerical Solution;235
9.7;3.7 Alternative Formulation of Boundary Element Method;265
9.8;3.8 Numerical Examples;272
10;Chapter 4. THERMOELASTICITY;290
10.1;4.1 Introduction;290
10.2;4.2 Governing Equations;292
10.3;4.3 Fundamental Solutions;305
10.4;4.4 Integral Representations of Displacements and Temperature;322
10.5;4.5 Integral Representations of Temperature Gradients and Stresses;333
10.6;4.6 Boundary Integral and Integro-Differential Equations;348
10.7;4.7 Numerical Implementation;364
10.8;4.8 Alternative BEM Formulation;402
10.9;4.9 Applications to Fracture Mechanics;417
10.10;4.10 Numerical Examples;435
11;Chapter 5. MICROPOLAR THERMOELASTICITY;454
11.1;5.1 Introduction;454
11.2;5.2 Equations of Motion;455
11.3;5.3 Fundamental Solutions in Three Dimensions;463
11.4;5.4 Fundamental Solutions for Plane Problems;477
11.5;5.5 Fundamental Solutions for Antiplane Problems;488
11.6;5.6 Integral Representations;493
11.7;5.7 BIE and BIDE;499
11.8;5.8 Applications to Fracture Mechanics;505
12;Chapter 6. ELASTOPLASTICITY;511
12.1;6.1 Introduction;511
12.2;6.2 Governing Equations;513
12.3;6.3 Boundary Integral Formulations;515
12.4;6.4 Elastoplastic Stress—Strain Relationships;529
12.5;6.5 Incremental Computations for Elastoplasticity;533
13;Chapter 7. VISCOELASTICITY;540
13.1;7.1 Introduction;540
13.2;7.2 Rheological Models and the Correspondence Principle;542
13.3;7.3 Boundary Integral Formulation;544
13.4;7.4 Schapery Inversion Algorithm;547
13.5;7.5 Applications to Fracture Mechanics;548
14;Chapter 8. THIN ELASTIC PLATES IN BENDING;557
14.1;8.1 Introduction;557
14.2;8.2 Governing Equations in Classical Plate Theory;558
14.3;8.3 Integral Formulation;567
14.4;8.4 Numerical Solution;581
14.5;8.5 Large Deflections. Berger Equation;591
14.6;8.6 Plates on Elastic Foundations;612
15;Chapter 9. STRESS ANALYSIS BY HYBRID METHODS;634
15.1;9.1 Introduction;634
15.2;9.2 Computation of Stresses at Internal Points from Stresses on Boundary;635
15.3;9.3 Combination of BIE with Holographic Interferometry Measurements;638
15.4;9.4 Hybrid Method in Fracture Mechanics;643
16;APPENDICES;646
16.1;Appendix A;646
16.2;Appendix B;649
16.3;Appendix C;658
16.4;Appendix D;660
16.5;Appendix E;665
16.6;Appendix F;678
16.7;Appendix G;685
17;REFERENCES;687
18;SUBJECT INDEX;696