Journal ArticleDOI
Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model
TLDR
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.read more
Citations
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Journal ArticleDOI
Current and future trends in topology optimization for additive manufacturing
Jikai Liu,Andrew T. Gaynor,Shikui Chen,Zhan Kang,Krishnan Suresh,Akihiro Takezawa,Lei Li,Junji Kato,Jinyuan Tang,Charlie C. L. Wang,Lin Cheng,Xuan Liang,Albert C. To +12 more
TL;DR: The motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics and the hope is to inspire both researchers and engineers to meet the challenges with innovative solutions.
Journal ArticleDOI
Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique
TL;DR: In this article, a non-probabilistic convex model is proposed to construct the multidimensional ellipsoids on the uncertainty, and a covariance matrix and correlation matrix can be created through all marginal convex models and covariances.
Journal ArticleDOI
Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models
TL;DR: In this paper, a non-probabilistic reliability-based topology optimization method for the design of continuum structures undergoing large deformation is presented. But the authors do not consider the nonlinearity of the structural system.
Journal ArticleDOI
Structural reliability analysis using non-probabilistic convex model
TL;DR: In this article, a non-probabilistic reliability model is given for structures with convex model uncertainty, which is defined as a ratio of the multidimensional volume falling into the reliability domain to the one of the whole model.
Journal ArticleDOI
Structural reliability analysis based on random distributions with interval parameters
TL;DR: In this article, two kinds of hybrid reliability models are constructed based on the reliability index approach (RIA) and the performance measurement approach (PMA), in which the reliable index interval and the target performance interval are employed to evaluate the reliability degree of an uncertain structure, respectively.
References
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Journal ArticleDOI
Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.
Book
Topology Optimization: Theory, Methods, and Applications
Martin P. Bendsøe,Ole Sigmund +1 more
TL;DR: In this article, the authors proposed a topology optimization by distribution of isotropic material for truss structures with anisotropic materials, based on the topology design of truss structure.
Journal ArticleDOI
The method of moving asymptotes—a new method for structural optimization
TL;DR: In this article, a new method for non-linear programming in general and structural optimization in particular is presented, in which a strictly convex approximating subproblem is generated and solved.
Journal ArticleDOI
Optimal shape design as a material distribution problem
TL;DR: In this article, various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable are described. But none of these methods can be used for shape optimization in a general setting.
Journal ArticleDOI
The COC algorithm, Part II: Topological, geometrical and generalized shape optimization
Ming Zhou,George I. N. Rozvany +1 more
TL;DR: In this paper, the COC algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members, and numerical results obtained are shown to be in close agreement with analytical results.