Méthode des équations intégrales régularisées en élastodynamique. (Regularized boundary integral equation method in elastodynamics). (French) Zbl 0612.73083

The classical boundary integral equations of elastostatics and elastodynamics, written in terms of Cauchy principal value singular integral operators, often lead to serious difficulties in numerical calculations. In order to surmount the problem, an approach, suitable for numerical applications, is proposed, consisting of a Cauchy principal value exclusion method which is applicable indifferently to bounded or unbounded domains. Two kinds of geometrical configurations are considered: (a) volumical obstacles (in unbounded media) or objects and (b) cracks. The boundary integral equations are rewritten in a form entirely free of Cauchy principal vaue integrals. Although the method is presented for three-dimensional linear elasticity, the principle remains valid for two dimensional elasticity or linear acoustics; the corresponding results are listed in the appendix.
The numerical efficiency of our method, with emphasis on the ”dynamics” and ”exterior problems” aspects, defining a preferential domain of application, is confirmed. Both construction and treatment of the boundary element-discretized problem are considered in detail. Our numerical results, for some tridimensional problems involving bounded as well as unbounded domains, show a good agreement with known analytical solutions.


74S30 Other numerical methods in solid mechanics (MSC2010)
65R20 Numerical methods for integral equations