H-DGTP—a Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures

Plates with ribs or stiffeners (stiffened plates) have been widely used as primary or secondary load bearing structures. Such structures could be fabricated by casting – a conventional yet important manufacturing process, their load bearing capacities are strongly dependent on the layout and sizes of the stiffeners. Thus it is necessary to establish specific topology optimization model and algorithm to obtain optimum layout, sizes and shapes of the stiffeners with casting constraints being considered. In this paper, we propose a new Heaviside-function based directional growth topology parameterization (H-DGTP) of the casting constraints for simultaneously optimizing the layout and height of the stiffeners. By using the new explicit parameterization, we can obtain a clear stiffener layout with optimized height. The differentiability of the parameterization is obtained by the use of a smooth approximation of the Heaviside function. In order to be applicable to a non-uniform mesh, a base surface is introduced and the minimum length of a stiffener can be controlled. Several numerical examples are presented to show the validity of this method.