Some aspects of the genesis of structures

Abstract

Bendsoe and Kikuchi (1988) introduced a novel approach of distributing mass within a specified design domain utilizing a stiffness-density relation obtained by homogenization of a cellular microstructure. This approach was extended to multiple loading cases and three-dimensional applications by the author and his associates (Mlejnek and Schirrmacher 1989; Mlejnek 1990). Moreover the well-known concept of explicit convex behaviour approximation together with a dual solution scheme (Fleury and Smaoui 1988) was successfully introduced to this problem. Further objectives such as eigenvalues and displacements generalized the range of application. It is the aim of this paper, to develop a simplified procedure that can be easily integrated into a FEM-analysis package. Its application requires essentially not much more than the usual FEM-technology. Nevertheless a traceable mathematical base is still maintained. A series of examples demonstrates the suitability of this approach to the preliminary design of minimal compliance structures made of isotropic materials.