Boundary Integral Equation Methods for Solids and Fluids

The boundary element method is more appropriate than the finite element method to tackle linear, wave propagation, infinite domain, mobile boundaries and unknown boundaries problems. In some engineering applications, both methods are combined. This book presents the mathematical basis of this method and its computer implementation. Numerous applications to fluid mechanics, mechanics of solids, acoustics and electromagnetism are developed.Das Design von Strukturen mittels BEM (Boundary Equation Methods) ist die Grundlage für zahlreiche Konstruktionsverfahren - Autos, Flugzeuge, Konzertsäle werden unter Anwendung dieser Methode entworfen. Der Autor - eine weltweit anerkannte Größe auf diesem Gebiet - behandelt die mathematischen Grundlagen und die Computersimulation dieses Verfahrens. (05/97) Basic principle and domains of application.

I. BOUNDARY INTEGRAL EQUATIONS FOR STATIC PROBLEMS : Integral Equations and Representations for the Poisson Equation;
Numerical Solution using Boundary Elements;
Integral Equations and Representations for Elastostatics;
Integral Representations of Gradients and Stresses on the Boundary;
Some Classical Mathematical Results

II. BOUNDARY INTEGRAL EQUATIONS FOR WAVE AND EVOLUTION PROBLEMS: Waves and Elastodynamics in Time Domain;
Waves and Elastodynamics in Frequency Domain;
Diffusion, Fluid Flow.

III. ADVANCED TOPICS : Variational Boundary Integral Formulations;
Exploitation of Geometrical Symmetry;
Domain Derivative and Boundary Integral Eequations.

IV. ADDITIONAL TOPICS IN SOLID MECHANICS : Boundary Integral Equations for Cracked Solids;
Initial Strain or Stress: Inclusions, Elastoplasticity.

APPENDICES : Tangential Differential Operators and Integration by Parts;
Interpolation Functions and Numerical Integration. Bibliography. Index. Aus dem Inhalt:
Basic Principles and Domains of Application;
I -
Boundary Integral Equations for Static Problems: Integral Equations and Representations for the Poisson Equation;
Numerical Solution Using Boundary Elements;
Integral Equations and Representations for Elastostatics;
Integral Representations of Gradients and Stresses on the Boundary;
Some Classical Mathematical Results;
II -
Boundary Integral Equations for Wave and Evolution Problems: Waves and Elastodynamics in Time Domain;
Waves and Elastodynamics in Frequency Domain;
Diffusion, Fluid Flow;
III -
Advanced Topics: Variational Boundary Integral Formulations;
Exploitation of Geometrical Symmetry;
Domain Derivative and Boundary Integral Equations;
IV -
Additional Topics in Solid Mechanics: Boundary Integral Equations for Cracked Solids;
Initial Strain or Stress Inclusions;
Elastoplasticity.

Marc Bonnet is the author of Boundary Integral Equation Methods for Solids and Fluids, published by Wiley. Going far beyond the standard texts, this book extensively covers boundary integral equation (BIE) formulations and the boundary element method (BEM). The first section introduces BIE formulations for potential and elasticity problems, following the modern regularization approach - the fundamental starting point for research in this field. Secondly, a clear description of BIE formulations for wave and elastodynamics problems, in both time and frequency domains is presented. Finally, recent research in the field, related to variational integral formulations, use of geometrical symmetry, shape sensitivity and fracture mechanics is summarised. Within the text a broad range of application areas, industrial as well as research related, are examined. These include:
* elasticity and small-strain elastoplasticity
* time-domain and frequency-domain scalar and elastic waves
* fracture mechanics
Including an extensive bibliography, this text will be of considerable value and interest to graduate students, researchers and lecturers in engineering mechanics, applied maths and physics, as well as industrial practitioners working within these areas.