simultaneous shape and reinforcement topology optimization of shell structures by using the method of moving asymptotes

this article is devoted to the simultaneous optimization of shape and topology of shell structures. the optimum shape is obtained together with the optimum layout for the reinforcement layers at the both sides of the shell surface. to solve this problem the finite element method is employed. it is assumed that each element is comprised of a porous media with microscopic rectangular voids where the density of the material in each element is a function of the geometric parameters of the voids. these parameters are also considered as the design variables of the topology optimization problem. the geometry of the shell structure is defined by using non-uniform rational b-splines (nurbs) technique and the control points of the nurbs’ surfaces are considered as the design variables of the shape optimization problem. for solution the method of moving asymptotes (mma) is employed. to demonstrate the efficiency of the method a few examples are presented and the results are discussed.