Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

Table 1

Comparison of robust and deterministic topology optimization design results.

Tests	Number of points	Mean	Standard deviation		Iterations	Time
Deterministic	1	22.36	12.03	0.25	54	35 s
Monte Carlo simulation	1000	21.37	11.13	0.25	55	302 s
Robust
Tensor product grid ()	9	22.26	11.85	0.25	51	59 s
Tensor product grid ()	25	21.87	11.66	0.25	54	90 s
Tensor product grid ()	81	21.77	11.34	0.25	54	147 s
Sparse grid ()	5	22.23	11.84	0.25	53	59 s
Sparse grid ()	13	21.92	11.70	0.25	54	68 s
Sparse grid ()	29	21.52	11.27	0.25	54	71 s