An efficient volume-preserving binary filter for additive manufacturing in topology optimization

Abstract

Topology optimization faces challenges concerning grey transition regions, manufacturability and computational efficiency. This article introduces an approach called the volume-preserving binary (VPB) filter. This novel sensitivity/density filter, based on a determinant-based matrix approach, efficiently detects grey elements and produces completely binary designs. The VPB filter addresses volume preservation by accurately expressing the volume-preserving condition, i.e. the volume before filtering equals the volume of solid materials after filtering. Comparison with other filtering methods, including the volume-preserving Heaviside filter and the Heaviside projection, illustrates the superior clarity and speed of the VPB filter. It reduces the number of iterations required for topology optimization, from hundreds or thousands to only tens of iterations, making it a promising solution for practical applications where manufacturability and computational efficiency are principal. Examples on compliance optimization, compliant mechanisms and heat conduction demonstrate the VPB filter's effectiveness in providing satisfactory solutions while perfectly preserving the length scale.