The method of fundamental solutions for axisymmetric elasticity problems
A method of fundamental solutions is proposed to obtain approximate solutions for axisymmetric boundary value problems of linear homogeneous isotropic elastostatics. The axially symmetric fundamental solutions for infinite body are represented in terms of complete elliptic integrals, and an approximate solution is expressed as a linear combination of fundamental solutions with singularities outside the domain of the problem, e.g., with singularities placed uniformly around the domain at a fixed distance along the normal to the boundary. The locations of these singularities and the coefficients of fundamental solutions in the linear combination are determined by a least square fit of boundary data. The method is illustrated by numerical solution of the problem for a finite cylinder under uniform axial tension and by numerical solution to the problem of torsion of a hollow finite cylinder subject to mixed boundary conditions. The authors also propose an extension of the method to examine axisymmetric bodies with non-axisymmetric boundary conditions.
linear homogeneous isotropic elastostatics
scientific article; zbMATH DE number 1491157