Semidefinite Programming For Uncertain Linear Equations In Static Analysis Of Structures

Yoshihiro Kanno; Izuru Takewaki

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Semidefinite Programming For Uncertain Linear Equations In Static Analysis Of Structures

机译：结构静态分析中不确定线性方程的半定规划

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This paper presents a method for computing a minimal bound that contains the solution set to the uncertain linear equations. Particularly, we aim at finding a bounding ellipsoid for static response of structures, where both external forces and elastic moduli of members are assumed to be imprecisely known and bounded. By using the g-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. Bounding ellipsoids are computed for nodal displacements of uncertain braced frames as the solutions of the presented SDP problems by using the primal-dual interior-point method.

机译：本文提出了一种计算最小界限的方法，其中包含不确定线性方程组的解。特别是，我们的目标是找到结构的静态响应的有界椭圆体，其中假定构件的外力和弹性模量都是未知的和有界的。通过使用g引理，我们制定了一个半定规划（SDP）问题，该问题提供了最小边界椭球的外部近似。通过使用原对偶内点法，对不确定支撑框架的节点位移计算出边界椭球，作为提出的SDP问题的解决方案。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2008年第1期|p.102-115|共14页
作者
Yoshihiro Kanno; Izuru Takewaki;
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作者单位

Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
关键词
semidefinite program; data uncertainty; uncertain linear equations; interval analysis; confidential bound; interior-point method;

机译：半定程序;数据不确定性;不确定线性方程组;区间分析;机密界;内点法;

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1. Semidefinite programming for dynamic steady-state analysis of structures under uncertain harmonic loads [J] . Yoshihiro Kanno, Izuru Takewaki Computer Methods in Applied Mechanics and Engineering . 2009,第41a44期

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2. A New Way of Using Semidefinite Programming with Applications to Linear Equations mod p [J] . Gunnar Andersson, Lars Engebretsen, Johan Hastad Journal of Algorithms . 2001,第2期

机译：半定规划及其在线性方程组中的应用的新方法mod p
3. A dynamical stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures [J] . Giovanni Falsone, Gabriele Ferro Structural Engineering and Mechanics . 2006,第6期

机译：基于矩方程的动力随机有限元法分析线性和非线性不确定结构
4. CONSTRUCTING LYAPUNOV FUNCTIONS FOR NONLINEAR DELAY-DIFFERENTIAL EQUATIONS USING SEMIDEFINITE PROGRAMMING [C] . Matthew Peet, Sanjay Lall IFAC Symposium on Nonlinear Control Systems . 2005

机译：使用SEMIDEFINITE编程构建用于非线性延迟微分方程的Lyapunov函数
5. Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations [D] . Sotoudeh, Zahra 2011

机译：使用完全本征方程的梁结构非线性静动力分析
6. Sparse nonnegative solution of underdetermined linear equations by linear programming [O] . David L. Donoho, Jared Tanner 2005

机译：线性规划的欠定线性方程组的稀疏非负解
7. Semidefinite programming for uncertain linear equations in static analysis of structures [O] . Kanno Yoshihiro, Takewaki Izuru 2008

机译：结构静态分析中不确定线性方程的半定规划
8. MODSAP: A Modified Version of the Structural Analysis Program SAP IV for the Static and Dynamic Response of Linear and Localized Nonlinear Structures [R] . Johnson, J. J. 1978

机译：mODsap：结构分析程序sap IV的修正版本，用于线性和局部非线性结构的静态和动态响应

Semidefinite Programming For Uncertain Linear Equations In Static Analysis Of Structures

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