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 薄板弯曲大变形高阶非线性偏微分方程推导与优化算法研究 Alternative Title Study on derivation and optimization algorithm about thin plate bending large deformation higher-order nonlinear partial differential equations 侯祥林; 郑夕健; 张良; 刘铁林; Hou, XL Source Publication 物理学报=Acta Physica Sinica 2012-09-23 Volume 61Issue:18Pages:180201 ISSN 1000-3290 Abstract 针对薄板弯曲大变形问题,运用变分原理,建立了薄板弯曲大变形问题的高阶非线性偏微分方程.运用有限差分法和动态设计变量优化算法原理,以离散坐标点的上未知挠度为设计变量,以离散坐标点的差分方程组构建目标函数,提出了薄板弯曲大变形挠度求解的动态设计变量优化算法,编制了相应的优化求解程序.分析了具有固定边界、均布载荷下的矩形薄板挠度的典型算例.通过与有限元的结果对比,表明了本文求解算法的有效性和精确性,提供了直接求解实际工程问题的基础. Other Abstract For a thin plate bending large deformation problem,variational principle is applied,and higher-order nonlinear partial differential equations about thin plate bending large deformation is established.Based on difference method and dynamic design variable optimization method,making unknown deflection of discrete coordinate points as design variables,differential equations sets of the discrete coordinates points as building objective function,a dynamic design variable optimization algorithm for computing thin plate bending deflection is proposed.Universal computing program is designed.Practical example about rectangular thin plate with fixed boundary under uniform load is analyzed.Comparing the program computing result with finite element solution.Effectiveness and feasibility of the method are verified.This method can be used to solve engineering problem. Keyword Higher-order Nonlinear Partial Differential Equations Thin Plate-bending Large Deformation Dynamic Design Variables Optimization Method Program Design Subject Area 结构力学 DOI 10.7498/aps.61.180201 URL 查看原文 Indexed By SCI ; CSCD Language 中文 WOS ID WOS:000311836700002 WOS Research Area Physics WOS Subject Physics, Multidisciplinary Funding Organization 国家自然科学基金(批准号:10972144);辽宁省自然科学基金(批准号:201102181);辽宁省教育厅科学研究项目(批准号:L2010445)资助的课题 CSCD ID CSCD:4652439 Citation statistics Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS] Document Type 期刊论文 Identifier http://dspace.imech.ac.cn/handle/311007/46649 Collection 流固耦合系统力学重点实验室 Corresponding Author Hou, XL Recommended CitationGB/T 7714 侯祥林,郑夕健,张良,等. 薄板弯曲大变形高阶非线性偏微分方程推导与优化算法研究[J]. 物理学报=Acta Physica Sinica,2012,61(18):180201. APA 侯祥林,郑夕健,张良,刘铁林,&Hou, XL.(2012).薄板弯曲大变形高阶非线性偏微分方程推导与优化算法研究.物理学报=Acta Physica Sinica,61(18),180201. MLA 侯祥林,et al."薄板弯曲大变形高阶非线性偏微分方程推导与优化算法研究".物理学报=Acta Physica Sinica 61.18(2012):180201.