Robust topology optimization under multiple independent unknown-but-bounded loads

Liu, Jian Tao; Gea, Hae Chang

doi:10.1016/j.cma.2017.09.033

Cited by 43 publications

(27 citation statements)

References 44 publications

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“…[46][47][48][49][50][51][52] This process can affect the reliability of equipment performance or even result in the failure of works. 12,[53][54][55][56][57][58][59][60][61] To enhance safety, many different uncertainty analysis and reliability evaluation approaches were proposed and developed in the past decades. In general, three types of these approaches are usually been utilized.…”

Section: Simulation or Approximation Reliability Methodsmentioning

confidence: 99%

Structural reliability analysis and uncertainties‐based collaborative design and optimization of turbine blades using surrogate model

Meng

Yang

Zhang³

et al. 2018

Fatigue Fract Eng Mat Struct

136

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In power and energy systems, both the aerodynamic performance and the structure reliability of turbine equipment are affected by utilized blades. In general, the design process of blade is high dimensional and nonlinear. Different coupled disciplines are also involved during this process. Moreover, unavoidable uncertainties are transported and accumulated between these coupled disciplines, which may cause turbine equipment to be unsafe. In this study, a saddlepoint approximation reliability analysis method is introduced and combined with collaborative optimization method to address the above challenge. During the above reliability analysis and design optimization process, surrogate models are utilized to alleviate the computational burden for uncertainties‐based multidisciplinary design and optimization problems. Smooth response surfaces of the performance of turbine blades are constructed instead of expensively time‐consuming simulations. A turbine blade design problem is solved here to validate the effectiveness and show the utilization of the given approach.

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Section: Simulation or Approximation Reliability Methodsmentioning

confidence: 99%

Structural reliability analysis and uncertainties‐based collaborative design and optimization of turbine blades using surrogate model

Meng

Yang

Zhang³

et al. 2018

Fatigue Fract Eng Mat Struct

136

View full text Add to dashboard Cite

show abstract

“…To this end, it was usually needed to determine the worst loading condition among all the possible uncertain loading positions with a lower‐level optimization formulation, and then the corresponding compliance sensitivities were utilized in Equation . However, it is important to note that this solution process for identifying the critical load case is extremely time consuming because the design objective of the lower‐level optimization problem is generally a nonconvex function …”

Section: Rto Algorithm With Load Position Uncertaintymentioning

confidence: 99%

“…From an engineering point of view, the final configuration design should be conducted judiciously in favor of the structural performance being less sensitive or immaterial to the possible variations of the loading conditions. Otherwise, the optimal structural properties obtained under the loading condition fixations may deteriorate drastically, and the layout design becomes vulnerable or even lead to catastrophic failures in the case of the loading uncertainties provided that the deterministic optimal solution has narrow margins of safety …”

Section: Introductionmentioning

confidence: 99%

“…For the past decades, structural topology optimization problems with consideration of load uncertainties have received increasing interests in the design optimization community. Thus far, a variety of approaches and techniques have been proposed to characterize the uncertain loadings in their various aspects, and a comprehensive study of the associated problems under the load magnitude and/or direction uncertainties has been made in the literature . Usually, these loading uncertainties are assumed as the uncertain‐but‐bounded design parameters, and then the optimal design problem is expressed to minimize the worst objective function induced by the uncertain loading conditions (worst‐case method).…”

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%

See 2 more Smart Citations

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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Game formulations for structural optimization under uncertainty

Thore

Grundström

Klarbring

2019

Numerical Meth Engineering

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Summary We consider structural optimization (SO) under uncertainty formulated as a mathematical game between two players –– a “designer” and “nature”. The first player wants to design a structure that performs optimally, whereas the second player tries to find the worst possible conditions to impose on the structure. Several solution concepts exist for such games, including Stackelberg and Nash equilibria and Pareto optima. Pareto optimality is shown not to be a useful solution concept. Stackelberg and Nash games are, however, both of potential interest, but these concepts are hardly ever discussed in the literature on SO under uncertainty. Based on concrete examples of topology optimization of trusses and finite element‐discretized continua under worst‐case load uncertainty, we therefore analyze and compare the two solution concepts. In all examples, Stackelberg equilibria exist and can be found numerically, but for some cases we demonstrate nonexistence of Nash equilibria. This motivates a view of the Stackelberg solution concept as the correct one. However, we also demonstrate that existing Nash equilibria can be found using a simple so‐called decomposition algorithm, which could be of interest for other instances of SO under uncertainty, where it is difficult to find a numerically efficient Stackelberg formulation.

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Robust topology optimization under multiple independent unknown-but-bounded loads

Cited by 43 publications

References 44 publications

Structural reliability analysis and uncertainties‐based collaborative design and optimization of turbine blades using surrogate model

Structural reliability analysis and uncertainties‐based collaborative design and optimization of turbine blades using surrogate model

Robust topology optimization under load position uncertainty

Game formulations for structural optimization under uncertainty

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