Shape optimization of thin walled structures governed by geometrically nonlinear mechanics

Firl, M.; Bletzinger, K.‐U.

doi:10.1016/j.cma.2012.05.016

Cited by 38 publications

(23 citation statements)

References 19 publications

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“…(5); however, the equilibrium equations are replaced by a Total Lagrangian finite element formulation for large displacements analysis. This modified optimization problem is often referred to as minimum end-compliance [15,29] since the objective function f = P T u no longer corresponds to the external work. In the following, linear compliance and nonlinear end-compliance are distinguished by adding a subscript to the notation: linear compliance is denoted by f l and nonlinear end-compliance by f nl .…”

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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show abstract

“…An summary on recent topology optimization techniques and applications in a variety of disciplines can be found in [59]. Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis is another geometric numerical modelling technique that optimizes form and material distribution either separately or simultaneously [60][61][62][63]. Other recent case studies on form-finding techniques support a variety of design innovation in structural forms which could achieve efficiency, economy, and elegance [64][65][66][67][68][69].…”

Section: Structural Principlesmentioning

confidence: 96%

Structural art: Past, present and future

Feng

Griffiths

2014

Engineering Structures

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“…The adjoint variable method is commonly used in the sensitivity analysis to resolve the former large-scale problem, and filtering techniques have been developed as smoothing solutions to the latter jagged shape problem. Among those techniques, Bletzinger et al proposed a mesh independent regularization method based on sensitivity filtering in the shape updating process [19][20][21][22]; Le et al introduced an shape filtering approach by filtering actual values of the design variables [23]; Hojjat et al reported a vertex morphing method to perform the out-of-plane filtering and in-plane mesh regularization operators simultaneously [24]. There are also filtering techniques as developed for CFD problems [25,26].…”

Section: Introductionmentioning

confidence: 98%

A non-parametric solution to shape identification problem of free-form shells for desired deformation mode

Liu¹,

Shimoda²

2014

Computers & Structures

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Shape optimization of thin walled structures governed by geometrically nonlinear mechanics

Cited by 38 publications

References 19 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

Structural art: Past, present and future

A non-parametric solution to shape identification problem of free-form shells for desired deformation mode

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