On the Dirichlet problem in elasticity for a domain exterior to an arc. (English) Zbl 0742.73026
The Dirichlet problem for the two-dimensional linear elasticity in the domain exterior to an open arc in the plane is considered. The problem is reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc. Existence, uniqueness and regularity conditions are established in appropriate Sobolev spaces. The asymptotic expansions concerning the singular behaviour for the solution near the tips of the arc are obtained. An augmented Galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi-optimal rate of convergence for the approximate solutions.
Reviewer: P.Puri (New Orleans)
MSC:
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 74B99 | Elastic materials |
| 74H99 | Dynamical problems in solid mechanics |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 74R99 | Fracture and damage |
| 35C20 | Asymptotic expansions of solutions to PDEs |
Keywords:
Garding’s inequality; two-dimensional linear elasticity; existence; uniqueness; Sobolev spaces; singular behaviour; solution near the tips; augmented Galerkin procedure; quasi-optimal rate of convergenceReferences:
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