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This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...
This paper is concerned with the computation of 3D vertex
singularities of anisotropic elastic fields with Dirichlet boundary
conditions, focusing on the derivation of error estimates for
a finite element method on graded meshes. The singularities are
described by eigenpairs of a corresponding operator pencil on
spherical polygonal domains. The main idea is to introduce a
modified quadratic variational boundary eigenvalue problem which
consists of two self-adjoint, positive definite sesquilinear...
We consider coupled structures consisting of two different linear elastic
materials bonded along an interface. The material discontinuities combined with
geometrical peculiarities of the outer boundary lead to unbounded stresses. The
mathematical analysis of the singular behaviour of the elastic fields,
especially near points where the interface meets the outer boundary, can be
performed by means of asymptotic expansions with respect to the distance from
the geometrical and structural singularities....
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