Applying functional principal components to structural topology optimization

Structural topology optimization aims to enhance the mechanical performance of a structure while satisfying some functional constraints. Nearly all approaches proposed in the literature are iterative, and the optimal solution is found by repeatedly solving a finite element analysis (FEA). It is thus clear that the bottleneck is the high computational effort, as these approaches require solving the FEA a large number of times. In this work, we address the need for reducing the computational time by proposing a reduced basis method that relies on functional principal component analysis (FPCA). The methodology has been validated considering a simulated annealing approach for compliance minimization in 2 classical variable thickness problems. Results show the capability of FPCA to provide good results while reducing the computational times, ie, the computational time for an FEA is about one order of magnitude lower in the reduced FPCA space.