On singularities of solutions of the displacement problem of linear elasticity near the vertex of a cone. (English) Zbl 0770.73014
Solutions of problems in three-dimensional elasticity in domains with conical boundary points exhibit singular behavior at these points. The singularity is crucially associated with the eigenvalues of a certain operator pencil on a domain cut out of the unit sphere by the tangent cone (not necessarily circular) to the boundary with vertex at the singular point. In this paper the first boundary-value problem of linearized elasticity is treated and a number of numerical features of the corresponding operator pencil spectrum are presented. In the particular case of a circular cone still more precise numerical results are given.
Reviewer: P.Laasonen (Helsinki)
MSC:
| 74B05 | Classical linear elasticity |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
three-dimensional elasticity; conical boundary points; eigenvalues; operator pencil; unit sphere; tangent coneReferences:
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