An expected compliance model based on topology optimization for designing structures submitted to random loads

Abstract

Abstract. In this paper, we focus in developing a stochastic model for topology optimization. The principal objective of such a model is to find robust structures for a given main load having a stochastic behavior. In the first part, we present the expected compliance formulation and some results in topology optimization. Then, in order to illustrate the interest of our approach, we consider a preliminary 3D cantilever benchmark experiment and compare the obtained results with the one given by a single load approach.

A New Compliance-function-shapeoriented Robust Approach for Volume-constrained Continuous Topology Optimization with Uncertain Loading Directions

“…Dunning et al [8] proposed a "pseudosample-based" stochastic method for considering loading directional uncertainty in topology optimization in order to produce robust solutions. Carrasco et al [9] presented a sample-based approach for the volume-constrained expected compliance minimization in topology optimization with stochastic loading directions. In the work of Liu et al [10] the directional uncertainty of the applied loads is described by directional interval variables which are divided into many small intervals, and then the uncertain small interval variables are approximated by their deterministic midpoints.…”

Robust Topology Optimization: A New Algorithm for Volume-constrained Expected Compliance Minimization with Probabilistic Loading Directions using Exact Analytical Objective and Gradient

“…The compliance expression is probabilistic one. Carrasco et al [12] presented a samplebased approach for the volume-constrained expected compliance minimization in topology optimization with stochastic load directions. In this paper, it was shown that the compliance minimization problem can be transformed into a standard multi-load topology optimization problem in which the loading scenarios are related to the variance of the random main load.…”