Surrogate Model Based on Proper Generalized Decomposition Method With Applications to Multiscale Topology Optimization

Based on the proper generalized decomposition (PGD) method, a surrogate model is proposed for parametrized numerical homogenization, and applied in multiscale topology optimization (TO). The proposed model accurately constructs a mapping from the geometric parameters of microstructures to their effective elasticity tensor. The major features include reduced storage requirements, higher computational efficiency, and no need for independent pointwise sampling over the parameter domain. Using such a surrogate model, a multiscale TO framework is presented under a volume fraction constraint of the matrix material. Three numerical examples illustrate the accuracy and efficiency of the proposed method in numerical homogenization. The corresponding multiscale TO results demonstrate its effectiveness.