Optimum shape design of mechanical structures (Sensitivity for discreted shape transformation)

Abstract

The method to obtain thee new sensitivities of shape optimization of mechanical structures are proposed to make possible to transform the structures precisely based on transposition of discreted elements using finite element method corresponding to the addition and removal of the elements. The new sensitivities are acquired by considering the changes of the nodal displacements after addition or removal of the elements in finite difference form which are far more suitable than the current one. The minimum weight problems are treated on cylindrical structures and two dimensional plate structures under constraints of equivalent stress. The obtained optimum structures are retransformed by smoothing procession using polynomials keeping the constraints and the minimalities of the weights.