Taylor series approximations for faster robust topology optimization

A means of reducing the computational cost in robust topology optimization is discussed. Without proper countermeasures, topology optimization can lead to artificially well-performing solutions for certain design problems, with unrealistic hinges that would break in reality. Enforcement of minimum length scales in both solid and void phases of the optimized designs mitigates this problem. The robust approach to topology optimization has been shown to produce designs that have such a two-phase minimum length scale. However, a drawback of the robust approach is the fact that multiple finite element analyses are needed per iteration step of the optimization, which slows down the optimization process. We therefore investigate the possibility of speeding up the computations by replacing some of the calculations based on finite element analyses with Taylor series approximations. Specifically, we consider first-, second-, third- and fourth-order Taylor series approximations of the objective functions of the dilated and eroded designs as a function of the projection threshold parameter. This robust approach with Taylor series approximations is tested by applying it to a compliant gripper design problem. It is shown that Taylor series approximations can be used to speed up the optimization process in robust topology optimization.