Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Journal of Computational Physics
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
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
On projection methods, convergence and robust formulations in topology optimization
Structural and Multidisciplinary Optimization
Heaviside projection based topology optimization by a PDE-filtered scalar function
Structural and Multidisciplinary Optimization
A new level-set based approach to shape and topology optimization under geometric uncertainty
Structural and Multidisciplinary Optimization
On the similarities between micro/nano lithography and topology optimization projection methods
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
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The aim of this paper is to introduce the stochastic collocation methods in topology optimization for mechanical systems with material and geometric uncertainties. The random variations are modeled by a memory-less transformation of spatially varying Gaussian random fields which ensures their physical admissibility. The stochastic collocation method combined with the proposed material and geometry uncertainty models provides robust designs by utilizing already developed deterministic solvers. The computational cost is discussed in details and solutions to decrease it, like sparse grids and discretization refinement are proposed and demonstrated as well. The method is utilized in the design of compliant mechanisms.