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Journal ArticleDOI

Robust topology optimization under material and loading uncertainties using an evolutionary structural extended finite element method

TL;DR: This paper is among the first to use the XFEM in studying the robust topology optimization under uncertainty and there is no need for any post-processing techniques, so the effectiveness of this method is justified by the clear and smooth boundaries obtained.
Abstract: This research presents a novel algorithm for robust topology optimization of continuous structures under material and loading uncertainties by combining an evolutionary structural optimization (ESO) method with an extended finite element method (XFEM). Conventional topology optimization approaches (e.g. ESO) often require additional post-processing to generate a manufacturable topology with smooth boundaries. By adopting the XFEM for boundary representation in the finite element (FE) framework, the proposed method eliminates this time-consuming post-processing stage and produces more accurate evaluation of the elements along the design boundary for ESO-based topology optimization methods. A truncated Gaussian random field (without negative values) using a memory-less translation process is utilized for the random uncertainty analysis of the material property and load angle distribution. The superiority of the proposed method over Monte Carlo, solid isotropic material with penalization (SIMP) and polynomial chaos expansion (PCE) using classical finite element method (FEM) is demonstrated via two practical examples with compliances in material uncertainty and loading uncertainty improved by approximately 11% and 10%, respectively. The novelty of the present method lies in the following two aspects: (1) this paper is among the first to use the XFEM in studying the robust topology optimization under uncertainty; (2) due to the adopted XFEM for boundary elements in the FE framework, there is no need for any post-processing techniques. The effectiveness of this method is justified by the clear and smooth boundaries obtained.
Citations
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01 Sep 2009
TL;DR: In this article, an efficient and accurate approach to robust structural topology optimization is proposed to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent.
Abstract: Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. This paper introduces an efficient and accurate approach to robust structural topology optimization. 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 new 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.

19 citations

Journal ArticleDOI
TL;DR: Wang et al. as mentioned in this paper proposed a feature-driven robust topology optimization strategy considering movable non-design domain and complex uncertainty, and the sensitivity of the robust optimization model is derived based on the shape derivative principle, which provides the basis for the implementation of gradient based optimization algorithm.

17 citations

Journal ArticleDOI
TL;DR: The Proportional Topology Optimization method renders the possibility of treating the stress constraints in a unified way, which allows topologies that at the same time preserve structural reliability and optimize costs.
Abstract: Topology optimization is a methodology widely used in the design phase that has gained space in engineering. On the other hand, uncertainty is present in material properties, loads, and boundary conditions in practically any design. The main goal for this paper lies in the coupling of the two subjects to account for uncertainties in the topology optimization. The Proportional Topology Optimization method renders the possibility of treating the stress constraints in a unified way. This allows topologies that at the same time preserve structural reliability and optimize costs. The Proportional Topology Optimization method under the reliability constraint is presented for isostatic and hyperstatic beam examples with stress and displacement LSF.

3 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed, which couples the level set method with the extended finite element method (X-FEM).

1,112 citations

Journal ArticleDOI
TL;DR: Reliability-Based Topology Optimization (RBTO) as mentioned in this paper integrates reliability analysis into topology optimization problems, in which reliability constraints are introduced into a deterministic top-ology optimization formulation.
Abstract: The objective of this work is to integrate reliability analysis into topology optimization problems. The new model, in which we introduce reliability constraints into a deterministic topology optimization formulation, is called Reliability-Based Topology Optimization (RBTO). Several applications show the importance of this integration. The application of the RBTO model gives a different topology relative to deterministic topology optimization. We also find that the RBTO model yields structures that are more reliable than those produced by deterministic topology optimization (for the same weight).

337 citations

Journal ArticleDOI
TL;DR: In this paper, a series of numerical examples are provided to answer the critical comments and show the validity and effectiveness of the evolutionary structural optimization method and compare BESO with other well-established optimization methods.
Abstract: Evolutionary Structural Optimization (ESO) and its later version bi-directional ESO (BESO) have gained widespread popularity among researchers in structural optimization and practitioners in engineering and architecture. However, there have also been many critical comments on various aspects of ESO/BESO. To address those criticisms, we have carried out extensive work to improve the original ESO/BESO algorithms in recent years. This paper summarizes latest developments in BESO for stiffness optimization problems and compares BESO with other well-established optimization methods. Through a series of numerical examples, this paper provides answers to those critical comments and shows the validity and effectiveness of the evolutionary structural optimization method.

299 citations

Journal ArticleDOI
TL;DR: In this article, a robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material properties is developed, which integrates the state-of-the-art level set methods for shape optimization and the latest research development in design under uncertainty.
Abstract: A robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material properties is developed in this work. The proposed approach integrates the state-of-the-art level set methods for shape and topology optimization and the latest research development in design under uncertainty. To characterize the high-dimensional random-field uncertainty with a reduced set of random variables, the Karhunen–Loeve expansion is employed. The univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is then employed for calculating statistical moments of the design response. The combination of the above techniques greatly reduces the computational cost in evaluating the statistical moments and enables a semi-analytical approach that evaluates the shape sensitivity of the statistical moments using shape sensitivity at each quadrature node. The applications of our approach to structure and compliant mechanism designs show that the proposed RSTO method can lead to designs with completely different topologies and superior robustness.

220 citations

Journal ArticleDOI
TL;DR: In this article, a quantified measure for non-probabilistic reliability based on the multi-ellipsoid convex model is proposed for topology optimization of continuum structures in the presence of uncertain-but-bounded parameters.
Abstract: Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization.

203 citations