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

Abstract

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.

Length scale and manufacturability in density-based topology optimization

“…Transformation of the constraints making them applicable to level set-based approaches are demonstrated in [154] and [155]. For the density based formulation, [54] has pro-posed an explicit parametrization for casting constraints based on a Heaviside projection which recently has been extended in [97]. An alternative is proposed in [67] where projection based algorithms have been utilized for imposing casting as well as milling constraints on topology optimized designs.…”

A component-based method for the optimization of stiffener layout on large cylindrical rib-stiffened shell structures

“…Luo and Gea (1998) used a second optimization step to find the optimal material orientations. Finally, Liu et al (2015) manage to obtain a stiffener-like topological shape by doing the topology optimization with 3D elements and casting process constraints. To facilitate the post-processing phase, methods using explicitly defined components have been developed, as reviewed by Wein et al (2020).…”

Topological Design of a Lightweight Sandwich Aircraft Spoiler

“…Zhu et al [19] proposed a novel TO method to improve the stiffness and strength of an aircraft skin stretch-forming die. A Heaviside-function-based directional growth topology parameterization has been developed to achieve stiffener layout designs [20], having the potential to design stiffener ribs for aircraft panels. Krog et al designed aircraft wing box ribs by using TO methods [21].…”