Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems

Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole; Jensen, Jakob Søndergaard

doi:10.1016/j.cma.2014.03.021

Cited by 190 publications

(164 citation statements)

References 24 publications

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“…One well-known issue is the occurrence of artificial instabilities in the void phase of the design domain which affect the convergence of the Newton-Raphson solver. Several strategies for solving this problem have been presented in the literature including modified material interpolation schemes [35], an element removal strategy [34] and the element connectivity parameterization method [36]. However, these instabilities mainly occur in structures that undergo very large displacements such as compliant mechanisms.…”

Section: Geometric Nonlinearitymentioning

confidence: 99%

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

Jansen

Lombaert

Schevenels

2015

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: M. Jansen, G. Lombaert, M. Schevenels, Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis, Comput. Methods Appl. Mech. Engrg. (2014), http://dx. AbstractTopology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections. Such imperfections might affect the structural stability and induce large displacement effects in these slender structures. This paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability. Geometric nonlinear effects are incorporated in the optimization by means of a Total Lagrangian finite element formulation in the minimization of endcompliance. Geometric imperfections are modeled as a vector-valued random field in the design domain. The resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem. These stochastic moments are typically estimated by means of sampling methods such as Monte Carlo simulation. However, these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm. An efficient solution algorithm which uses adjoint differentiation in a second-order perturbation method is therefore developed to estimate the stochastic moments during the optimization. Two applications with structures that exhibit different types of structural instabilities are examined. In both cases, it is demonstrated by means of an extensive Monte Carlo simulation that the deterministic design is very sensitive to imperfections, while the design obtained my means of the proposed method is much more robust.

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Section: Geometric Nonlinearitymentioning

confidence: 99%

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

Jansen

Lombaert

Schevenels

2015

Computer Methods in Applied Mechanics and Engineering

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“…In pursuing more realistic designs, continuous efforts have been conducted to extend topology optimization to nonlinear structural designs considering various sources of nonlinearity, such as geometrical nonlinearity (e.g., Buhl et al 2000;Gea and Luo 2001;Pedersen et al 2001;Bruns and Tortorelli 2003;Yoon and Kim 2005;Wang et al 2014;Luo et al 2015), material nonlinearity (e.g., Yuge and Kikuchi 1995;Bendsøe et al 1996;Maute et al 1998;Yuge et al 1999;Schwarz et al 2001;Yoon and Kim 2007;Bogomolny and Amir 2012), and both geometrical and material nonlinearities simultaneously (e.g., Jung and Gea 2004;Huang and Xie 2008).…”

Section: Introductionmentioning

confidence: 99%

Evolutionary topology optimization of elastoplastic structures

Xia

Fritzen

Breitkopf

2016

Struct Multidisc Optim

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We have recently proposed in (Fritzen et al., Int J Numer Methods Eng 106 (6): 2016) an evolutionary topology optimization model for the design of multiscale elastoplastic structures, which is in general independent of the applied material law. Facing the variability of the final design for minor parameter changes when dealing with plastic structural designs, we further improve the robustness and the effectiveness of the BESO optimization procedure in this work by introducing a damping scheme on sensitivity numbers and by progressively reducing the sensitivity filtering radius. The damping scheme constraining the variance of the sensitivity numbers stabilizes the topological evolution process in particular for dissipative structural designs. By setting initially a large filter radius value and reducing it gradually, the emergence of the redundant structural branches, which are to be eliminated afterwards and Liang Xia are the main reasons deteriorating the design process, could be avoided. The robustness and the effectiveness of the improved model has been validated by means of benchmark numerical examples of conventional homogeneous structures.

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“…To more closely obtain a distinct 0‐1 design, a Heaviside thresholding technique() and material penalization are combined. First, the continuous filtered density

\overset{c}{true}

is thresholded using a smoothed Heaviside step function H ∗ , according to

c = H^{*} false(\overset{c}{true} false) = \frac{\tanh false(β_{H} ω false) + \tanh ((), β_{H} false(\overset{c}{true} - ω false))}{\tanh false(β_{H} ω false) + \tanh ((), β_{H} false(1 - ω false))},

where c ∈ [0, 1] is deemed the physical volume fraction field.…”

Section: Regularization and Materials Interpolationmentioning

confidence: 99%

Topology optimization of finite strain viscoplastic systems under transient loads

Ivarsson

Wallin

Tortorelli

2018

Numerical Meth Engineering

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Summary A transient finite strain viscoplastic model is implemented in a gradient‐based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark‐beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.

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Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems

Cited by 190 publications

References 24 publications

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

Robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis

Evolutionary topology optimization of elastoplastic structures

Topology optimization of finite strain viscoplastic systems under transient loads

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