APPLICATIONS OF BOUNDARY-ELEMENT METHODS TO PROBLEMS IN MECHANICS

This exploratory lecture gives an overview of the applications of boun dary element methods to a class of fundamental problems in mechanics. Both linear and nonlinear problems are included. In particular, topics are drawn from the areas of potential flow for exterior boundary valu e problems, contact problems in elasticity for problems with nonlinear boundary conditions, and fluid-solid interactions for transmission pr oblems. These topics in some sense cover basic mathematical formulatio ns of boundary integral equations with side conditions, boundary varia tional inequalities as well as the coupling Of the finite element and boundary element methods for inhomogeneous multi-media with linear and nonlinear material. Emphases are given to the mathematical foundation s of the methods, their physical interpretations of various side condi tions in the formulations and to the unique solvability of variational equations of the problems.