An efficient method for topology optimization of continuum structures in the presence of uncertainty in loading direction

Published on Oct 1, 2017in International Journal of Computational Methods2.193
路 DOI :10.1142/S0219876217500542
Jie Liu12
Estimated H-index: 12
(Hunan University),
Guilin Wen23
Estimated H-index: 23
(Hunan University)
+ 1 AuthorsYi Min Xie69
Estimated H-index: 69
(RMIT: RMIT University)
Sources
Abstract
This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.
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For the purpose of improving structural dynamic reliability, a topological optimization methodology for maximizing the dynamic response reliability index is proposed based on the bi-directional evolutionary structural optimization (BESO) method. The objective of the present study is to maximize the dynamic response reliability index at specified points on the structure under random excitation, subject to volume constraints on multi-phase materials over the admissible design domain. The sensitivi...
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This contribution presents a computationally efficient method for reliability-based topology optimization for continuum domains under material properties uncertainty. Material Young's modulus is assumed to be lognormally distributed and correlated within the domain. The computational efficiency is achieved through estimating the response statistics with stochastic perturbation of second order, using these statistics to fit an appropriate distribution that follows the empirical distribution of th...
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This paper reports an efficient approach for uncertain topology optimization in which the uncertain optimization problem is equivalent to that of solving a deterministic topology optimization problem with multiple load cases. Probabilistic and fuzzy property of the directional uncertainty of the applied loads is considered in the topology optimization; the cloud model is employed to describe that property which can also take the correlations of the probability and fuzziness into account. Converg...
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Novel robust truss topology optimization with material and loading uncertainties.Spatially correlated material stiffness across truss included in problem formulation.Spectral stochastic finite element analysis, taking truss element length into account.Multiobjective approach to generate robust Pareto optimal solutions.Examples show effects of novel truss material modelling on the robust optimal designs. In this paper an approach to robust topology optimization for truss structures with material ...
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