Revisiting element removal for density-based structural topology optimization with reintroduction by Heaviside projection

We present a strategy grounded in the element removal idea of Bruns and Tortorelli (2003) aimed at reducing computational cost circumventing potential numerical instabilities density-based topology optimization. The design variables relative densities are both represented on fixed, uniform finite grid, linked through filtering Heaviside projection. regions analysis domain where density is below specified threshold removed from forward replaced by nodal boundary conditions. This brings progressive cut as optimization proceeds helps to mitigate associated with low-density regions. Removed can be readily reintroduced since all remain active modeled formal sensitivity analysis. A key feature proposed approach that projection promotes material reintroduction along structural boundaries amplifying magnitude sensitivities inside filter reach. Several 2D 3D examples presented, including linear nonlinear compliance minimization, force inverter, frequency buckling load maximization. shown effective producing optimized designs equivalent or nearly those obtained without removal, while providing remarkable savings.