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  

Study on derivation and optimization algorithm about thin plate bending large deformation higher-order nonlinear partial differential equations

作　　者：侯祥林[1] 郑夕健[1] 张良[2] 刘铁林[3] 

机构地区：[1]沈阳建筑大学交通与机械工程学院,沈阳110168 [2]中国科学院力学研究所,北京100080 [3]沈阳建筑大学土木工程学院,沈阳110168

出　　处：《物理学报》2012年第18期9-18,共10页Acta Physica Sinica

基　　金：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~~

摘　　要：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.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 optimiza- tion 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.

关 键 词：高阶非线性偏微分方程 薄板弯曲大变形 动态设计变量优化算法 程序设计 

分 类 号：O347[理学—固体力学] O175.29[理学—力学]