Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Efficient topology optimization in MATLAB using 88 lines of code
Structural and Multidisciplinary Optimization
On projection methods, convergence and robust formulations in topology optimization
Structural and Multidisciplinary Optimization
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
Eliminating beta-continuation from Heaviside projection and density filter algorithms
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
On the similarities between micro/nano lithography and topology optimization projection methods
Structural and Multidisciplinary Optimization
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The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty. A sampling method is used to estimate these statistics during the optimization process. The proposed method is successfully applied to three example problems: the minimum compliance design of a slender column-like structure and a cantilever beam and a compliant mechanism design. An extensive Monte Carlo simulation is used to show that the obtained topologies are more robust with respect to geometric imperfections.