Shape optimization of truss-stiffened shell structures with variable thickness

This paper presents an effective approach to shape optimal design of statically loaded elastic shell-like structures. The shape parametrization is based on a design element technique. The chosen design element is a rational Bézier body, enhanced with a smoothly varying scalar field. A body-like design element makes possible to unify the shape optimization of both pure shells and truss-stiffened shell structures. 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 linear and non-linear analysis of shell structures, a reliable 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. Four numerical examples of shell and truss-stiffened shell optimization are presented in detail to illustrate the performance of the proposed approach.