Mixed crack type problem in anisotropic elasticity. (English) Zbl 0901.73016
Summary: We consider a three-dimensional mixed boundary value problem of the anisotropic elasticity theory when the elastic body under consideration has a cut in the form of an arbitrary non-closed two-dimensional smooth surface with a smooth boundary: on one side of the cut surface the Dirichlet type condition (i.e., the displacement vector) is given, while on the other side the Neumann type condition (i.e., the stress vector) is prescribed. Applying the potential method and the theory of PsDEs uniqueness, existence and regularity results are proved in various function spaces. The asymptotic expansion of the solution of the corresponding system of boundary PsDEs is written out.
MSC:
| 74B99 | Elastic materials |
| 74H99 | Dynamical problems in solid mechanics |
| 74R99 | Fracture and damage |
| 74E10 | Anisotropy in solid mechanics |
| 35Q72 | Other PDE from mechanics (MSC2000) |
Keywords:
three-dimensional boundary value problem; non-closed two-dimensional smooth surface; Dirichlet type condition; Neumann type condition; potential method; theory of PsDEs uniqueness; existence; regularity; function spacesReferences:
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