Shape optimization of shell structures with variable thickness

This paper presents an effective approach to shape optimal design of statically loaded elastic shell structures. The shape parameterization is based on a design element technique. The chosen design element is a rational Bezier body, enhanced with a smoothly varying scalar field. The scalar field of the design element is obtained by attaching to each control point a scalar quantity, which is an add-on to the position and weight of the control point. This scalar field is linked to the shell thickness distribution, which can be optimized simultaneously with the shape of the shell. For the analysis of the structure a nonlinear 4-node shell finite element formulation is utilized. The presented optimization approach assumes the employment of a gradient-based optimization algorithm and the use of the discrete method of direct differentiation to perform the sensitivity analysis. A numerical example is presented to illustrate the performance of the proposed approach.