Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

Table 2

Comparison of robust and deterministic topology optimization design results.

Tests	Number of points	Mean	Standard deviation		Iterations	Time
Deterministic	1	241.08	131.42	0.06	44	7 min 14 s
Monte Carlo simulation	1000	182.20	111.34	0.06	51	28 min 27 s
Robust
Tensor product formula ()	9	183.95	121.71	0.06	46	8 min 19 s
Tensor product formula ()	25	182.62	119.30	0.06	49	9 min 44 s
Tensor product formula ()	81	182.91	113.72	0.06	49	17 min 26 s
Sparse grid method ()	5	183.20	122.66	0.06	47	8 min 18 s
Sparse grid method ()	13	182.71	119.24	0.06	50	8 min 47 s
Sparse grid method ()	29	182.93	114.02	0.06	50	10 min 25 s