3-D Shell Topology Optimization Using a Design Domain Method

Gea, Hae Chang; Fu, Yong

doi:10.4271/951105

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…In the Voigt mixing rule, usage of isostrain conditions (7) gives an e ective Young's modulus of the mixture as (11) Similarly, using the Reuss isostress assumption (3.2) gives an e ective Young's modulus for the mixture as…”

Section: Special Case: Linear Isotropic Solid and Void Materialsmentioning

confidence: 99%

“…An alternative relaxed formulation based on an assumed micro-morphology in the material layout is the Mori-Tanaka mixing rule employed by Gea. 11 The Mori-Tanaka mixing rule 12 is based on the physical assumption of dilute suspensions of ellipsoidal particles of material A embedded in a matrix of material B and uses analytical Eshelby solutions 13 to predict the elastic properties of the mixtures based solely on the volume fraction and assumed particle shapes and orientations of the respective phases. This mixing rule can in principle be used in inelastic topology optimization since its usage for inelastic materials is already established as, for example, in the constitutive modelling of elastoplastic particulate composites.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Voigt-Reuss topology optimization for structures with linear elastic material behaviours

Swan

Kosaka

1997

Int. J. Numer. Meth. Engng.

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The desired results of variable topology material layout computations are stable and discrete material distributions that optimize the performance of structural systems. To achieve such material layout designs a continuous topology design framework based on hybrid combinations of classical Reuss (compliant) and Voigt (sti ) mixing rules is investigated. To avoid checkerboarding instabilities, the continuous topology optimization formulation is coupled with a novel spatial ÿltering procedure. The issue of obtaining globally optimal discrete layout designs with the proposed formulation is investigated using a continuation method which gradually transitions from the sti Voigt formulation to the compliant Reuss formulation. The very good performance of the proposed methods is demonstrated on four structural topology design optimization problems from the literature.

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Section: Special Case: Linear Isotropic Solid and Void Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Voigt-Reuss topology optimization for structures with linear elastic material behaviours

Swan

Kosaka

1997

Int. J. Numer. Meth. Engng.

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“…[15][16][17] In the so-called 'structural topology optimization' a ÿxed spatial design domain D is designated as a subset of a full structural domain S , and optimal spatial material distributions throughout D are determined. Many variable topology material layout optimization frameworks today feature continuous formulations of the problem, in which either amorphous mixtures or microstructured mixtures (composites) are permitted to reside throughout D in intermediate and even ÿnal design states.…”

Section: Overviewmentioning

confidence: 99%

Voigt-Reuss topology optimization for structures with nonlinear material behaviors

Swan

Kosaka

1997

Int. J. Numer. Meth. Engng.

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This work is directed toward optimizing concept designs of structures featuring inelastic material behaviours by using topology optimization. In the proposed framework, alternative structural designs are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain. Since two or more materials are permitted to simultaneously occupy local regions of the design domain, small-strain integration algorithms for general two-material mixtures of solids are developed for the Voigt (isostrain) and Reuss (isostress) assumptions, and hybrid combinations thereof. Structural topology optimization problems involving non-linear material behaviours are formulated and algorithms for incremental topology design sensitivity analysis (DSA) of energy type functionals are presented. The consistency between the structural topology design formulation and the developed sensitivity analysis algorithms is established on three small structural topology problems separately involving linear elastic materials, elastoplastic materials, and viscoelastic materials. The good performance of the proposed framework is demonstrated by solving two topology optimization problems to maximize the limit strength of elastoplastic structures. It is demonstrated through the second example that structures optimized for maximal strength can be signiÿcantly di erent than those optimized for minimal elastic compliance. ?

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Stiffener layout optimization of shell structures with B-spline parameterization method

Feng

Zhang

Meng

et al. 2021

Struct Multidisc Optim

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3-D Shell Topology Optimization Using a Design Domain Method

Cited by 4 publications

References 9 publications

Voigt-Reuss topology optimization for structures with linear elastic material behaviours

Voigt-Reuss topology optimization for structures with linear elastic material behaviours

Voigt-Reuss topology optimization for structures with nonlinear material behaviors

Stiffener layout optimization of shell structures with B-spline parameterization method

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