SEMIANALYTICAL SINGULAR ELEMENT AND ITS APPLICATION TO STRESS CALCULATION AND OPTIMIZATION

A semianalytical singular element is proposed to model the stress fiel ds in plane and axisymmetric elastic bodies in the vicinity of singula r 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. Intro duction of specially generated shape functions in the approximating ex pressions for displacements enables one to ensure the displacement com patibility with the standard elements. A detailed consideration is giv en to the convergence of the finite-element procedure. The extensive p ossibilities of the proposed singular element are exemplified by solvi ng particular elastic problems. The applicability of the elaborated si ngular element is discussed with respect to optimization of geometry a nd material properties in the vicinity of singular points. Two optimiz ation problems are presented to illustrate a search for the body geome try providing the optimal stress distribution.