An improved adaptive constraint aggregation for integrated layout and topology optimization

• We present an improved adaptive constraint aggregation approach based on the KS function.
• Steffensen iteration is used to obtain better aggregation parameters.
• The improved approach is applied with the finite circle method to avoid the components’ overlap in integrated layout and topology optimization design.
• Multi-point constraints (MPC) are applied to establish the interconnections between movable components and supporting structures.
• The improved approach can handle the constraint aggregation and the integrated optimization well.

The purpose of this paper is to present a Kreisselmeier–Steinhauser (KS) function based adaptive constraint aggregation approach. It is implemented within the integrated layout and topology optimization of multi-component structure systems to avoid using large numbers of non-overlapping constraints defined by means of the previously proposed finite circle method (FCM). An improved adaptive approach is then put forward to obtain proper aggregation parameters for the KS function based constraint aggregation, contributing to less numerical difficulties while meeting the same aggregation precision compared with the existing adaptive approach. Furthermore, the complex step derivative approximation is utilized to yield better sensitivities for the aggregated constraint functions with high nonlinearity. Moreover, during the integrated layout and topology optimization, multi-point constraints (MPC) are applied to establish the interconnections between movable components and supporting structures, which can use fixed finite element meshes and analytical sensitivities. Finally, some numerical examples are tested to demonstrate the validity and effectiveness of the proposed formulation.