| Abstract: | This paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies. While the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method (FEM), this is far from true for the boundary element method (BEM). The primary reason for this fact is that the axisymmetric kernels in the integral equations of the BEM contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape. Thus, special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements. The accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge.A successful numerical implementation of the boundary element method with elementwise (called the Mixed approach) or pointwise (called the pure BEM or BEM approach) determination of stress rates has been carried out. A computer program has been developed for the solution of general axisymmetric viscoplasticity problems. Comparisons of numerical results from the BEM and FEM, for several illustrative problems, are presented and discussed in the paper. It is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross-section, and these solutions are also compared with the BEM and FEM results for such cases. |
