Voigt-Reuss topology optimization for structures with nonlinear material behaviors

Swan, Colby C.; Kosaka, Iku

doi:10.1002/(sici)1097-0207(19971030)40:20<3785::aid-nme240>3.0.co;2-v

Cited by 93 publications

(26 citation statements)

References 36 publications

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“…However, there are limited studies in topology optimization considering material nonlinearities. An attempt to include von Mises elastoplasticity in topology optimization was first made by Swan and Kosaka , wherein interpolation schemes based on Voigt‐Reuss type mixing rules were used. Maute et al and Schwarz et al considered a Solid Isotropic Material with Penalization (SIMP)‐like interpolation with von Mises plasticity for maximizing ductility in topology optimization and an approximate sensitivity analysis was utilized.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of energy absorbing structures with maximum damage constraint

Zhang

Khandelwal

2017

Numerical Meth Engineering

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A novel density-based topology optimization framework for plastic energy absorbing structural designs with maximum damage constraint is proposed. This framework enables topologies to absorb large amount of energy via plastic work before failure occurs. To account for the plasticity and damage during the energy absorption, a coupled elastoplastic ductile damage model is incorporated with topology optimization. Appropriate material interpolation schemes are proposed to relax the damage in the low-density regions while still ensuring the convergence of Newton-Raphson solution process in the nonlinear finite element analyses. An effective method for obtaining path-dependent sensitivities of the plastic work and maximum damage via adjoint method is presented, and the sensitivities are verified by the central difference method. The effectiveness of the proposed methodology is demonstrated through a series of numerical examples.to the recent review studies [12,14]. Among these available methods, the density-based method is perhaps the most popular one, which is also the subject of this study.Most of the studies concerning density-based topology optimization are based on linear or nonlinear elastic material, with applications to stiffness designs, compliant mechanisms, and fundamental frequency designs [10,13,[22][23][24][25]. Energy absorption is an irreversible process and is accompanied by various inelastic material dependent mechanisms. To account for such inelastic material response, inelastic constitutive models should be considered in topology optimization for designing energy absorbing structures. However, there are limited studies in topology optimization considering material nonlinearities. An attempt to include von Mises elastoplasticity in topology optimization was first made by Swan and Kosaka [26], wherein interpolation schemes based on Voigt-Reuss type mixing rules were used. Maute et al. [27] and Schwarz et al.[28] considered a Solid Isotropic Material with Penalization (SIMP)-like interpolation [29] with von Mises plasticity for maximizing ductility in topology optimization and an approximate sensitivity analysis was utilized. Later on, Bogomolny and Amir [30] combined the Drucker-Prager elastoplasticity with topology optimization for conceptual maximum stiffness reinforced concrete structure designs and the adjoint method proposed by Michaleris et al. [31] was used for the sensitivity analysis. Kato et al. [32] eliminated the simplifications used in references [27,28] to obtain more accurate analytical sensitivities for multiphase material topology optimization with von Mises elastoplasticity. Nakshatrala and Tortorelli [33] proposed a topology optimization framework for energy dissipation maximization subjected to impact loadings wherein the material response was modeled with von Mises plasticity. Wallin et al. [34] extended the von Mises plasticity to finite strain scenario for maximum plastic work designs. Recently, the authors also incorporated anisotropic Hoffmann plasticity model in topology o...

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Section: Introductionmentioning

confidence: 99%

Topology optimization of energy absorbing structures with maximum damage constraint

Zhang

Khandelwal

2017

Numerical Meth Engineering

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“…Those nonlinear effects can appear at the material (Swan and Kosaka 1997) and/or at the geometrical levels (Buhl et al 2000) where so-called post-buckling and collapse scenarios are studied. Including such nonlinearities makes the problem much more intricate since both the optimization task and the structural analysis are nonlinear.…”

Section: Fig 1 Structural Optimization Problemsmentioning

confidence: 99%

Optimization methods for advanced design of aircraft panels: a comparison

et al. 2009

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Advanced nonlinear analyses developed for estimating structural responses for recent applications for the aerospace industry lead to expensive computational times. However optimization procedures are necessary to quickly provide optimal designs. Several possible optimization methods are available in the literature, based on either local or global approximations, which may or may not include sensitivities (gradient computations), and which may or may not be able to resort to parallelism facilities. In this paper Sequential Convex Programming (SCP), Derivative Free Optimization techniques (DFO), Surrogate Based Optimization (SBO) and Genetic Algorithm (GA) approaches are compared in the design of stiffened aircraft panels with respect to local and global instabilities (buckling and collapse). The computations are carried out with software developed for the European aeronautical industry. The specificities of each optimization method, the results obtained, computational time considerations and their adequacy to the studied problems are discussed.

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“…The third example stems from an application initially suggested by Swan and Kosaka [24] to demonstrate that ultimate strength optimization can lead to substantially different results from a minimum elastic compliance design. In the present study the same example is revisited in the framework of first failure stress constraints and elastic behavior.…”

Section: Four-bar Truss Problemmentioning

confidence: 99%

Topology and generalized shape optimization: Why stress constraints are so important?

Duysinx

Miegroet

Lemaire

et al. 2008

Int. J. Simul. Multidisci. Des. Optim.

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-The paper continues along the work initiated by the authors in taking into account stress constraints in topology optimization of continuum structures. Revisiting some of their last developments in this field, the authors point out the importance of considering stress constraints as soon as the preliminary design phase, that is, to include stress constraints in the topology optimization problem in order to get the most appropriate structural layout. Numerical applications that can be solved using these new developments make possible to exhibit interesting results related to the specific nature of strength based structural layout for maximum strength compared to maximum stiffness. This particular character of stress design is clearly demonstrated in two kinds of situations: once several load cases are considered and when unequal stress limits in tension and compression are involved.

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Voigt-Reuss topology optimization for structures with nonlinear material behaviors

Cited by 93 publications

References 36 publications

Topology optimization of energy absorbing structures with maximum damage constraint

Topology optimization of energy absorbing structures with maximum damage constraint

Optimization methods for advanced design of aircraft panels: a comparison

Topology and generalized shape optimization: Why stress constraints are so important?

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