SEMIANALYTICAL SINGULAR ELEMENT AND ITS APPLICATION TO STRESS CALCULATION AND OPTIMIZATION

A semianalytical singular element is proposed to model the stress fields in plane and axisymmetric elastic bodies in the vicinity of singular points. The element generation is performed, taking into account the structure of analytical solution in the vicinity of such points. This renders the element well suited for any type of singular points. Introduction of specially generated shape functions in the approximating expressions for displacements enables one to ensure the displacement compatibility with the standard elements. A detailed consideration is given to the convergence of the finiteelement procedure. The extensive possibilities of the proposed singular element are exemplified by solving particular elastic problems. The applicability of the elaborated singular element is discussed with respect to optimization of geometry and material properties in the vicinity of singular points. Two optimization problems are presented to illustrate a search for the body geometry providing the optimal stress distribution.