<p>An alternative and cheaper way of designing structures with reduced sensitivity to manufacturing variations and uncertainties in topology optimization is investigated. Established robustness schemes involve optimizing with multiple design realizations, stochastic gradients or complex perturbations approaches. Motivated by the observation that conventional deterministic designs exhibit sharp peaks in their sensitivity fields, meaning high susceptibility to uncertainties, a simple yet computationally efficient remedy is proposed. The proposed method augments the original objective with a smooth maximum of the element-wise physical design sensitivities, directly penalizing excessive local sensitivity and promoting smoother distributions. This indirectly reduces sensitivity to manufacturing variations and uncertainties, at the cost of only one additional adjoint load for compliance minimization and three for general objectives, all using the same factorization as the primal solve. Numerical studies demonstrate that the proposed formulation significantly reduces sensitivity hot spots, improves robustness to manufacturing variations, and resolves hinge localization in compliant mechanism design, all with minimal degradation of the nominal objective. The new approach that has close ties to previously studied first-order second moment approaches is named “sensitivity hot spot penalization".</p>

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Towards robust topology optimization by penalization of sensitivity hot spots

  • Ole Sigmund

摘要

An alternative and cheaper way of designing structures with reduced sensitivity to manufacturing variations and uncertainties in topology optimization is investigated. Established robustness schemes involve optimizing with multiple design realizations, stochastic gradients or complex perturbations approaches. Motivated by the observation that conventional deterministic designs exhibit sharp peaks in their sensitivity fields, meaning high susceptibility to uncertainties, a simple yet computationally efficient remedy is proposed. The proposed method augments the original objective with a smooth maximum of the element-wise physical design sensitivities, directly penalizing excessive local sensitivity and promoting smoother distributions. This indirectly reduces sensitivity to manufacturing variations and uncertainties, at the cost of only one additional adjoint load for compliance minimization and three for general objectives, all using the same factorization as the primal solve. Numerical studies demonstrate that the proposed formulation significantly reduces sensitivity hot spots, improves robustness to manufacturing variations, and resolves hinge localization in compliant mechanism design, all with minimal degradation of the nominal objective. The new approach that has close ties to previously studied first-order second moment approaches is named “sensitivity hot spot penalization".