Premium
Three‐dimensional singularities of elastic fields near vertices
Author(s) -
Schmitz Hermann,
Volk Klaus,
Wendland Wolfgang
Publication year - 1993
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690090309
Subject(s) - mathematics , gravitational singularity , mathematical analysis , mellin transform , vertex (graph theory) , piecewise , galerkin method , eigenvalues and eigenvectors , boundary (topology) , finite element method , fourier transform , combinatorics , graph , physics , quantum mechanics , thermodynamics
For the computation of the singular behavior of an elastic field near a three‐dimensional vertex subject to displacement boundary conditions we use a boundary integral equation of the first kind whose unknown is the boundary stress. Localization at the vertex and Mellin transformation yield a one‐dimensional integral equation on a piecewise circular curve γ in IR 3 depending holomorphically on the complex Mellin parameter. The corresponding spectral points and packets of generalized eigenvectors characterize the desired stress field and are computed by a spline‐Galerkin method with graded meshes at the corner points of the curve γ. © 1993 John Wiley & Sons, Inc.