A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

Abstract

Structural topology optimization (STO) is usually treated as a constrained minimization problem, which is iteratively addressed by solving the equilibrium equations for the problem under consideration. To reduce the computational effort, several reduced basis approaches that solve the equilibrium equations in a reduced space have been proposed. In this work, we apply functional principal component analysis (FPCA) to generate the reduced basis, and we couple FPCA with a gradient-based optimization method for the first time in the literature. The proposed algorithm has been tested on a large STO problem with 4.8 million degrees of freedom. Results show that the proposed algorithm achieves significant computational time savings with negligible loss of accuracy. Indeed, the density maps obtained with the proposed algorithm capture the larger features of maps obtained without reduced basis, but in significantly lower computational times, and are associated with similar values of the minimized compliance.

From Stress to Shape: Equilibrium of Cloister and Cross Vaults

“…In other engineering application, however, the shape of structures is optimized under the constraints of material saving, or compliance minimization. This is the case of the Structural Topology Optimization [30], used for optimally distribute the material to minimize the compliance o structures under given loads [31][32][33]. Optimization is also used in geotechnical applications [34], optimization of geodesic domes [35], of soil-steel structures [36], and lightweight structure [37]…”