SIMP type topology optimization procedure considering uncertain load position

Abstract

IntroductionThe topology optimization has more than 100 years of history and still it is an expanding field in structural optimization. The numerical procedure for FE (finite element) based topology optimization of continuum type of structures was elaborated first by Rossow and Taylor [19] in 1973, but the real expansion started at the end of 80-s [4,20]. The majority of the papers still deal with deterministic problems. During these years several optimal topologies were numerically calculated but the analytical confirmations -which have come recently (Rozvany [21], Sokółet. al [22]) -are mostly missing. Until the end of the last century almost one could not find any publication on topology optimization considering uncertainties.During the last years before the millennium almost there were no publications in the topic of probability based topology optimization. The stochastic optimization works of Marti and Stöckl [16,17] provide early information about this topic. The paper of Duan et al. [5] is among the very first publications in the field of uncertainty based topology optimization. This work presents an entropy-based topological optimization method for truss structures by the use of iteration technique. Also a truss topology optimization (layout optimization) of the object of the paper of Alvarez and Carrasco [1] in case stochastic loading. They showed mathematically that a problem of finding the truss of minimum expected compliance (stability of the members are not considered) under stochastic loading conditions is equivalent to the dual of a special convex minimax problem. Dunning et al. [6,7] introduce an efficient and accurate approach to robust structural topology optimization for continuum type of problems. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level-set-based topology optimization method are then used to demonstrate the proposed approach.Topology optimization with uncertainty in the magnitude and

Parametric Study on the Element Size Effect for Optimal Topologies

“…During its hundred years of history it has become clear that the non-unique solution property of the method is affected by the material parameters (Poisson ratio) and the ways of the discretization. The applied finite element technique and the selected type of finite elements (generally four-nodes quadrilateral elements are used) can overcome numerical difficulties [9,[10][11][18][19]. From the very first start of the numerical solution technique of topology optimization, a serious problem with it was the erroneous appearance of corner contacts between solid elements in the solution (checkerboards, diagonal element chains, isolated hinges).…”

Optimal design of curved folded plates

“…The formulations above can lead to the same optimal solution as if the objective function and the compliance constraint were interchanged. Another slight modification has to be evaluated if multiple loading and/or stochastic loading (Lógó [11,12]) is considered. Either the number of the compliance constraint is increased or the objective function (45) has to be modified to form a min-max problem.…”

“…The design methods generally elaborated on deterministic based data but later it was extended to stochastic ones (e.g. Lógó [12]). …”

Robust topology optimization of thin plate structure under concentrated load with uncertain load position

“…Hashimoto and Kanno [Hashimoto and Kanno, 2015] considered the uncertainty of node location for a truss topology [Tada and Seguchi, 1989] investigated the effects of the uncertainty of the load position on the shape design of basic two-dimensional continua. Lógó [Lógó, 2012] proposed a robust design considering uncertain load position for a continuous topology design problem, in which the load magnitude is modeled as a spatially probabilistic distributed load but the load position remains fixed.…”