Applying functional principal components to structural topology optimization [1]

Structural Topology Optimization optimizes 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 Elements 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 the Functional Principal Component Analysis (FPCA). The methodology has been validated considering a Simulated Annealing approach for the compliance minimization in a variable thickness cantilever sheet. Results show the capability of FPCA to provide good results while reducing the computational times, i.e., the computational time for a FEA analysis is about one order of magnitude lower in the reduced FPCA space.