Efficient Multimodes Monte Carlo Method for Structural Topology Optimization With Random Uncertainties

Structural topology optimization with random material or boundary load requires significant computational costs in solving numerous random elastic systems, particularly in 3D. Based on the multimode representation of displacement and the Monte Carlo method for sampling the probability space, a phase field model is proposed for robust topology optimization, where Young's modulus and the applied loading are characterized as random fields. The optimization algorithm is proposed based on the gradient flow scheme and the multimode Monte Carlo method. The well-posedness and truncation error estimates of the multimode Monte Carlo method have been rigorously discussed. Numerical examples of compliance minimization and compliant mechanisms in both 2D and 3D show the proposed algorithm's accuracy, effectiveness, and efficiency for robust topology optimization.