Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Held, Harald

doi:10.1007/978-3-8348-9396-3

Cited by 2 publications

(1 citation statement)

References 87 publications

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“…[14,[18][19][20][21][22][23][24][25][26]). As a part of the robust design for uncertain loads, the stiffness maximization under the worst load case in a set of prescribed uncertain loads is investigated.…”

Section: Introductionmentioning

confidence: 98%

Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system

Takezawa

Nii

Kitamura

et al. 2011

Computer Methods in Applied Mechanics and Engineering

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a b s t r a c tThis paper proposes a topology optimization for a linear elasticity design problem subjected to an uncertain load. The design problem is formulated to minimize a robust compliance that is defined as the maximum compliance induced by the worst load case of an uncertain load set. Since the robust compliance can be formulated as the scalar product of the uncertain input load and output displacement vectors, the idea of ''aggregation'' used in the field of control is introduced to assess the value of the robust compliance. The aggregation solution technique provides the direct relationship between the uncertain input load and output displacement, as a small linear system composed of these vectors and the reduced size of a symmetric matrix, in the context of a discretized linear elasticity problem, using the finite element method. Introducing the constraint that the Euclidean norm of the uncertain load set is fixed, the robust compliance minimization problem is formulated as the minimization of the maximum eigenvalue of the aggregated symmetric matrix according to the Rayleigh-Ritz theorem for symmetric matrices. Moreover, the worst load case is easily established as the eigenvector corresponding to the maximum eigenvalue of the matrix. The proposed structural optimization method is implemented using topology optimization and the method of moving asymptotes (MMA). The numerical examples provided illustrate mechanically reasonable structures and establish the worst load cases corresponding to these optimal structures.

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Section: Introductionmentioning

confidence: 98%

Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system

Takezawa

Nii

Kitamura

et al. 2011

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

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A Review on Optimization Literature Related to Operations Research Field

Pulat

Bayyurt

Kocakoç

2020

Dokuz Eylül Üniversitesi Sosyal Bilimler Enstitüsü Dergisi

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Optimization is an iterative search process aimed at finding the best solution value for an objective function that satisfies constraints or bounded conditions in mathematically expressible problems. There are hundreds of books written in this field, and a new book is added to the list everyday. Since optimization is a very large field, each book is written for different disciplines. If you want to work on any subject related to this field, reaching the related book can be complicated and time consuming. The point to be reached in the research is to do an extensive research on the optimization books and to obtain relevant statistics. For this purpose, available optimization books related to the operations research of the last ten years were searched and examined in detail according to their topics. This work is aiming at leading the people who want to study about this topic by searching the literature about the optimization in the field of operations research.

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Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Cited by 2 publications

References 87 publications

Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system

Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system

A Review on Optimization Literature Related to Operations Research Field

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