Gradient-based multi-component topology optimization for stamped sheet metal assemblies (MTO-S)

This paper presents a continuous relaxation of our previous work on the multi-component topology optimization, which enables the use of efficient gradient-based optimization to attain the simultaneous optimization of a base structural topology and its decomposition. In addition to the fictitious material density used in the classic SIMP method, new design variables specifying fractional membership to each component are introduced, in order to relax the process of decomposing a candidate structural topology into a discrete number of components. The concept of joint stiffness is also relaxed using the new component membership variables. Considering stamped sheet metal assemblies jointed by the resistance spot-welding, the stamping die cost consists of die-set material cost and die machining cost. The former is modeled as the minimum bounding box area enclosing each component, approximated by a product of weighted variances in major and minor directions obtained by a weighted principal component analysis. The latter is modeled as an empirical shape complexity index similar to the one available in the literature. Examples on compliance minimization of multi-component sheet metal assemblies are presented, where the proposed continuous relaxation formulation solved by a gradient-based optimization algorithm generated comparable results with dramatically improved computational efficiency over our previous results by discrete formulations solved by the genetic algorithm.

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