Deterministic versus reliability-based topology optimization of aeronautical structures

López, Carlos; Baldomir, Aitor; Hernández, Santiago

doi:10.1007/s00158-015-1363-4

Cited by 22 publications

(15 citation statements)

References 26 publications

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“…As we know, there are generally two main approaches often used to deal with the topology optimization problems under uncertainties: RBTO and RTO, respectively. 7,13,[23][24][25][26] From the aforementioned illustration, it is recognized that the loading position of F 1 is an uncertain-but-bounded parameter to the structural layout design. Usually, the precise statistical…”

Section: Description Of the Application Point Uncertainty Of An Extermentioning

confidence: 99%

“…Therefore, the probability distribution (or density) function of the load position becomes really unavailable in practical problems. Besides, it has been often shown that the result of the reliability‐based topology optimization (RBTO) is rather sensitive to the actual probability distributions of the uncertain design parameters . Practically, an external load is often expected to act within a small region near a specific spot on a structure even though its true loading point is virtually unknown or uncontrollable.…”

Section: Introductionmentioning

confidence: 99%

“…1,3 It is widely known that, in the preliminary design phase of an engineering structure, there inevitably exist a large number of uncertainties associated not only with the structural parameters, for instance, the physical properties of the materials, 4-7 geometry dimensions, 8,9 but also with the external applied loads for lack of the detailed information about the real loading conditions in practice. 7,[10][11][12][13][14][15][16][17] That is, a part or all of the external loads imposed on the structural model cannot be determined specifically in their magnitudes, directions, and/or locations in the early conceptual design stage. Besides, during the whole service lifetime of a practical structure, an external applied load may experience changes or variations, to a certain extent, in its application situation because of the complicated loading environments.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, it has been often shown that the result of the reliability-based topology optimization (RBTO) is rather sensitive to the actual probability distributions of the uncertain design parameters. 7,13,21 Practically, an external load is often expected to act within a small region near a specific spot on a structure even though its true loading point is virtually unknown or uncontrollable. For this reason, a nonprobabilistic approach seems to provide a more attractive scheme for exploring the RTO problem with the uncertain load position.…”

Section: Introductionmentioning

confidence: 99%

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Robust topology optimization under load position uncertainty

Wang

Gao

2019

Numerical Meth Engineering

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Summary The topology optimization problem of a continuum structure on the compliance minimization objective is investigated under consideration of the external load uncertainty in its application position with a nonprobabilistic approach. The load position is defined as the uncertain‐but‐bounded parameter and is represented by an interval variable with a nominal application point. The structural compliance due to the load position deviation is formulated with the quadratic Taylor series expansion. As a result, the objective gradient information to the topological variables can be evaluated efficiently in a quadratic expression. Based on the maximum design sensitivity value, which corresponds to the most sensitive compliance to the uncertain loading position, a single‐level optimization approach is suggested by using a popular gradient‐based optimality criteria method. The proposed optimization scheme is performed to gain the robust topology optimizations of three benchmark examples, and the final configuration designs are compared comprehensively with the conventional topology optimizations under the loading point fixation. It can be observed that the present method can provide remarkably different material layouts with auxiliary components to accommodate the load position disturbances. The numerical results of the representative examples also show that the structural performances of the robust topology optimizations appear less sensitive to the load position perturbations than the traditional designs.

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Section: Description Of the Application Point Uncertainty Of An Extermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust topology optimization under load position uncertainty

Wang

Gao

2019

Numerical Meth Engineering

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“…This includes applying RBTO to large 3D problems including wing ribs and a tail cone structure using the SORA approach [30]. Another approach combined the Hybrid Cellular Automaton (HCA) algorithm with PMA [31].…”

mentioning

confidence: 99%

Reliability-Based Topology Optimization with Analytic Sensitivities

Clark

Patil

2018

2018 AIAA Non-Deterministic Approaches Conference

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(Academic)Reliability-Based Design Optimization (RBDO) approaches often use the First-Order Reliability Method (FORM) to efficiently obtain an estimate of the reliability of a system. This approach treats the reliability analysis as a nested optimization problem, where the objective is to compute the most probable point (MPP) by minimizing the distance between the failure surface and the origin of a normalized random space. Numeric gradient calculation of the solution of this nested problem requires an additional solution of the FORM problem for each design variable, an approach which quickly becomes computationally intractable for large scale problems including Reliability-Based Topology Optimization (RBTO). In this thesis, an alternative analytic approach to the analysis and sensitivity of nested optima derived from the Lagrange Multiplier Theorem is explored. This approach leads to a system of nonlinear equations for the MPP analysis for any given set of design variables. Taking the derivative of these equations with respect to a design variable gives a linear system of equations in terms of the implicit sensitivities of the MPP to the design variable where the coefficients of the linear equations depend only on the current MPP. By solving this system, these sensitivities can be obtained It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or unmodeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the

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Robust topology optimization under multiple independent uncertainties of loading positions

Wang

Gao

2020

Numerical Meth Engineering

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The topology optimization problem of a continuum structure is further investigated under the independent position uncertainties of multiple external loads, which are now described with an interval vector of uncertain-but-bounded variables. In this study, the structural compliance is formulated with the quadratic Taylor series expansion of multiple loading positions. As a result, the objective gradient information to the topological variables can be evaluated efficiently upon an explicit quadratic expression as the loads deviate from their ideal application points. Based on the minimum (largest absolute) value of design sensitivities, which corresponds to the most sensitive compliance to the load position variations, a two-level optimization algorithm within the non-probabilistic approach is developed upon a gradient-based optimization method. The proposed framework is then performed to achieve the robust optimal configurations of four benchmark examples, and the final designs are compared comprehensively with the traditional topology optimizations under the loading point fixation. It will be observed that the present methodology can provide a remarkably different structural layout with the auxiliary components in the design domain to counteract the load position uncertainties. The numerical results also show that the present robust topology optimization can effectively prevent the structural performance from a noticeable deterioration than the deterministic optimization in the presence of load position disturbances.

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Deterministic versus reliability-based topology optimization of aeronautical structures

Cited by 22 publications

References 26 publications

Robust topology optimization under load position uncertainty

Robust topology optimization under load position uncertainty

Reliability-Based Topology Optimization with Analytic Sensitivities

Robust topology optimization under multiple independent uncertainties of loading positions

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