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Full Description
Boundary Element Analysisbehind the boundary element method and its computer applications. The author uses Cartesian tensor notation throughout the book and includes the steps involved in deriving many of the equations, enabling students to master this powerful and necessary tool for comprehending most of the literature on boundary elements. The book reviews elasticity, plate bending, elastodynamics, and elastoplasticity theories and their boundary element formulations. The author provides computer programs in Fortran 77 for elastostatic, plate bending, and free and forced vibration problems with detailed descriptions of various segments of the code. He adopts a unified approach in developing these programs, so that when students understand of the working of one program, they can easily follow the others. This approach enables students to begin using the boundary element method immediately. The book also presents a brief description of the finite element method with steps to develop efficient computer codes and a number of ways to combine the boundary element and finite boundary element equations to achieve the best results when analyzing a variety of engineering problems. The author's elegant presentation and comprehensive coverage of problems in structural and solid mechanics make Boundary Element Analysis: Theory and Programming an easy-to-use text for both students and professors.
Contents
MEET THE BOUNDARY ELEMENT METHODWhat is the Boundary Element Method?How the Method WorksDirect and Indirect Boundary Element MethodsBoundary Element Method versus Finite Element MethodA Brief History of the Boundary Element MethodELASTOSTATIC PROBLEMSIntroductionBrief Review of the Mathematical Theory of ElasticityTwo-Dimensional Problems of ElasticityThe Reciprocal Theorem and the Somogliana IdentityBoundary Integral EquationNumerical Solution of Boundary Integral EquationsBoundary Elements and Interpolation of Displacements and TractionsStresses on the BoundaryBody ForcesPiecewise Homogeneous BodiesModelling Traction DiscontinuitiesSolids of RevolutionAnistropic ElasticityBOUNDARY ELEMENTS, INTERPOLATION FUNCTIONS, AND SINGULAR INTEGRALSIntroductionTwo-Dimensional ProblemsThree-Dimensional ProblemsDiscontinuous Boundary ElementsCOMPUTER CODES FOR TWO DIMENSIONAL IntroductionFortran Code with Two-Noded Linear Boundary ElementsFortran Code with Three-Noded Isoparametric Quadratic Boundary ElementsSample ProblemsAn Improved Boundary Integral Formulation with Relative Displacements ElastostaticsPLATE BENDING PROBLEMSIntroductionReview of Thin Plate Flexure TheoryThe Boundary Integral Equations for Plate FlexureFundamental SolutionsSurface LoadsNumerical ImplementationCOMPUTER CODE FOR PLATE BENDING PROBLEMSIntroductionFortran Code with Two-Noded Linear Boundary ElementsSample ProblemsELASTODYNAMIC PROBLEMSIntroductionFree Vibration ProblemsForces Vibration ProblemsCOMPUTER CODES FOR TWO-DIMENSIONAL ELASTODYNAMIC PROBLEMSIntroductionFortran Code for Free Vibration ProblemsFortran Code for Forced Vibration ProblemsELASTOPLASTIC PROBLEMSIntroductionSome PreliminariesBrief Review of the Theory of PlasticityGoverning Equations of ElastoplasticityBoundary Element Formulations Involving Volume IntegrationElastoplastic Boundary Element Formulation using Particular IntegralsNumerical ImplementationIterative AlgorithmIntroductionIntroduction to Finite Element MethodCoupling of Finite Element and Boundary Element SolutionsAn Example Problem-Analysis of Reinforced Concrete Structural ElementsAppendix A: Integral EquationsA.1. Definition and Classification of Integral EquationsA.2 Cauchy Principle Value of an IntegralAppendix B: Numerical IntegrationB.1 Standard Gauss QuadratureB.2 Logarithmic Gauss QuadratureAppendix C: Fundamental SolutionC.1 Three-Dimensional Laplace EquationC.2 Two-Dimensional Laplace Equation
