Robust topology optimization of compliant mechanisms with uncertainties in output stiffness

Abstract

Summary This work addresses the topology optimization approach to design robust compliant mechanisms with respect to uncertainties in the output stiffness, when compared to the traditional deterministic approach. To this end, two formulations are proposed: probabilistic and nonprobabilistic. The probabilistic formulation minimizes a joint objective function of expected output displacement plus a measure of its standard deviations, for given statistical distribution of the output stiffness. The nonprobabilistic formulation is written as minimization of a joint function of the median of output displacements, plus the width of the intervals that contains the extreme values of the output displacements, for a given interval of output stiffness. The Monte Carlo simulation method is used to evaluate expected values and standard deviations of output displacements in the probabilistic formulation and to assess results obtained with the deterministic approach. It is shown that both formulations lead to designs where output displacements are less sensitive to variations of output stiffness when compared to the traditional deterministic approach. Furthermore, as an additional benefit, it is observed that large variations of output stiffness can hinder the appearance of one‐node connected hinges, usually found in the deterministic design of compliant mechanisms.

Multi-material topology optimization of compliant mechanisms using regularized projected gradient approach

“…4 The difference of the values of volume fraction of first and second material with their prescribed values in the optimization process material, and it is illustrated that the algorithm can manage these as well. For future work, it is recommended to investigate the ability of the approach in the consideration of the uncertainty in the output stiffness which is demonstrated to be so important [47]. 6 Identified topologies for the cases presented in Table 3.…”

Momentum‐based accelerated mirror descent stochastic approximation for robust topology optimization under stochastic loads

“…Several remarks can be made regarding the above entropic AC‐MDSA update. First, the derived update (26) and (27) can handle both positive and negative stochastic gradients, thus it is also applicable to RTO problems with other objective functions, such as the compliant mechanism design 12,19 . Second, as long as the initial guess is in the feasible domain, the (and ) always stays positive.…”

“…While the classical setting of topology optimization assumes problem‐related parameters that are deterministic, real‐world structures are subjected to various sources of randomness, such as load, material property, and geometry, which can influence the layout of optimized designs. Thus, robust topology optimization (RTO) has been employed to improve the robustness of designs concerning random sources 8‐19 …”

Momentum-based Accelerated Mirror Descent Stochastic Approximation for Robust Topology Optimization under Stochastic Loads

“…Several remarks can be made regarding the above entropic AC-MDSA update. First, the derived update ( 26) and ( 27) can handle both positive and negative stochastic gradients, thus it is also applicable to RTO problems with other objective functions, such as the compliance mechanism design [12,19]. Second, as long as we start from a feasible initial guess, the xk (and x k ) always stays positive.…”

“…While the classical setting of topology optimization assumes problem-related parameters that are deterministic, real-world structures are subjected to various sources of randomness, such as load, material property, and geometry, which can influence the layout of optimized designs. Thus, robust topology optimization (RTO) has been employed to improve the robustness of designs concerning random sources [8,9,10,11,12,13,14,15,16,17,18,19].…”