Optimization of slender structures considering geometrical imperfections

Baitsch, Matthias; Hartmann, Dietrich

doi:10.1080/17415970600573494

Cited by 9 publications

(6 citation statements)

References 14 publications

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“…It is assumed that the structure is placed correctly on the supports, i.e., geometric imperfections are zero at the location of the supports. These constraints can be incorporated in the description of the random field by means of a conditional random field [41,42]. The conditional distribution of a Gaussian random field given some known values in a set of points {x i ∈ Ω|i ∈ 1, .…”

Section: Geometric Imperfectionsmentioning

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 Imperfectionsmentioning

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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“…finite element model) as variables subjected to uncertainty. This approach has for example been successfully applied to model geometric imperfections in robust shape optimization problems (Baitsch and Hartmann, 2006) and robust truss topology optimization problems (Guest and Igusa, 2008). Such an approach can be denoted as a Lagrangian type method since the computational grid (i.e.…”

Section: Misplacement and Misalignment Of Materialsmentioning

confidence: 99%

“…These assumptions can be accounted for using a conditioned random field based on random field interpolation using linear regression (Ditlevsen, 1996). This approach has been applied by several authors to model random fields of geometrical imperfections (Baitsch and Hartmann, 2006;Kolanek and Jendo, 2008). In the Gaussian case, the method is equivalent to replacing the random field by a conditional random field with known values.…”

Section: Random Fields With Known Valuesmentioning

confidence: 99%

“…Misalignment of material has already been considered in several structural optimization problems. Baitsch and Hartmann (2006) used random perturbations of the nodal locations in order to model geometric imperfections in the shape optimization of truss structures. In truss topology optimization, Guest and Igusa (2008) modeled misalignment of material by perturbing the nodal locations of the ground structure.…”

Section: Introductionmentioning

confidence: 99%

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Robust topology optimization accounting for misplacement of material

Jansen

Lombaert

Diehl

et al. 2012

Struct Multidisc Optim

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The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined

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“…The term derives from the fuzzy sets theory (Zadeh, 1965). In civil engineering, FSs are applied in problems that require analysis in presence of uncertainty: some noteworthy applications concern the structural design (Biondini et al, 2004; Malekly et al, 2009), structural reliability (Dordoni et al, 2010), structural control (Kim et al, 2010), risk analysis (Sadeghi et al, 2010), and the treatment of uncertainties (Möller et al, 2003; Sgambi, 2004; Baitsch and Hartmann, 2006; Tagherouit et al, 2011; Wang and Li, 2011).…”

Section: Introductionmentioning

confidence: 99%

Genetic Algorithms for the Dependability Assurance in the Design of a Long‐Span Suspension Bridge

Sgambi

Gkoumas

Bontempi

2012

Computer aided Civil Eng

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A long-span suspension bridge is a complex structural system that interacts with the surrounding environment and the users. The environmental actions and the corresponding loads (wind, temperature, rain, earthquake, etc.) together with the live loads (railway traffic, highway traffic), have a strong influence on the dynamic response of the bridge, and can significantly influence the structural behavior and alter its geometry, thus limiting the serviceability performance even up to a partial closure. This article will present some general considerations and operative aspects of the activities related to the analysis and design of such a complex structural system. Specific reference is made to the dependability assessment and the performance requirements of the whole system, while focus is given on methods for handling the completeness and the uncertainty in the assessment of the load scenarios. Aiming at the serviceability assessment, a method based on the combined application of genetic algorithms and a finite element method (FEM) investigation is proposed and applied

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Optimization of slender structures considering geometrical imperfections

Cited by 9 publications

References 14 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

Robust topology optimization accounting for misplacement of material

Genetic Algorithms for the Dependability Assurance in the Design of a Long‐Span Suspension Bridge

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