Topology optimization of structures with geometrical nonlinearities

Gea, Hae Chang; Luo, Jie

doi:10.1016/s0045-7949(01)00117-1

Cited by 98 publications

(57 citation statements)

References 20 publications

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“…While such an approach is very straightforward in principle, a complicating factor is that when the buckling eigenvalues of the structure are nonsimple ͑repeated͒, their design derivatives are discontinuous. Accordingly, an alternative approach to designing stable, sparse structures in a continuum topology framework is to model the structure as an elastic continuum taking into account finite deformation effects and the associated instabilities ͑Buhl et al 2000; Bruns and Tortorelli 2001;Gea and Luo 2001;Rahmatalla and Swan 2003͒. Nevertheless, the advantage of the first approach over the latter is its substantially lower computational cost.…”

Section: Introductionmentioning

confidence: 99%

Form Finding of Sparse Structures with Continuum Topology Optimization

Rahmatalla

Swan

2003

J. Struct. Eng.

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A continuum topology optimization methodology suitable for finding optimal forms of large-scale sparse structures is presented. Since the need to avoid long compressive spans can be critical in determining the optimal form of such structures, a formulation is used wherein the structure is modeled as a linear elastic continuum subjected to design loads, and optimized in form to maximize the minimum critical buckling load. Numerical issues pertinent to accurate solution of the linearized buckling eigenvalue problem and accurate design sensitivity analysis are discussed. The performance of the proposed design formulation is demonstrated on a few problems designed to find optimal forms of a canyon bridge, long-span bridges, and an electrical transmission tower. In all cases, very credible structural forms are obtained with the proposed design formulation. The results of the design examples solved are typically superior structural forms with regard to buckling stability than those obtained to minimize the mean structural compliance.

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Section: Introductionmentioning

confidence: 99%

Form Finding of Sparse Structures with Continuum Topology Optimization

Rahmatalla

Swan

2003

J. Struct. Eng.

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“…Because of the transformations, a new measure for stress, the second Piola-Kirchhoff stress tensor, has to be introduced with the Green-Lagrange strain tensor. Considering TL formulation for a general body subjected to applied body forces f B and surface tractions f S on the surface S and displacement field δu i , the equation of motion is given by (Gea and Luo 2001) …”

Section: Geometrically Nonlinear Behaviour Of a Continuum Bodymentioning

confidence: 99%

“…The Green-Lagrange strain tensor, which is defined with respect to the initial configuration of the body, is given by (Gea and Luo 2001) …”

Section: Geometrically Nonlinear Behaviour Of a Continuum Bodymentioning

confidence: 99%

“…Transforming the continuous form of the equation of motion represented by Equation (15) to an FE formulation, the equilibrium equation is obtained as (Gea and Luo 2001;Bathe 2006) …”

Section: Finite Element Formulationmentioning

confidence: 99%

“…However, if snapthrough effects are involved in the problems, the difference could be significant. Gea and Luo (2001) proposed a microstructure-based design approach with a nonlinear FE formulation for the topology optimization of structures with geometric nonlinearity. Pedersen, Buhl, and Sigmund (2001) considered topology optimization of nonlinear compliant mechanisms represented with frame elements.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Abdi

Ashcroft

Wildman

2018

Engineering Optimization

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. ABSTRACTThe topology optimization using isolines/isosurfaces and extended finite element method (Iso-XFEM) is an evolutionary optimization method developed in previous studies to enable the generation of high-resolution topology optimized designs suitable for additive manufacture. Conventional approaches for topology optimization require additional postprocessing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this timeconsuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this article, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated. ARTICLE HISTORY

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Topology Optimization of Nonlinear Continuum Structures

Huang

Xie

2010

Evolutionary Topology Optimization of Continuum Structures

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Topology optimization of structures with geometrical nonlinearities

Cited by 98 publications

References 20 publications

Form Finding of Sparse Structures with Continuum Topology Optimization

Form Finding of Sparse Structures with Continuum Topology Optimization

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Topology Optimization of Nonlinear Continuum Structures

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