一种分析柔性梁超大挠度问题的小波算法  

A WAVELET METHOD FOR STUDYING LARGE DEFLECTION BENDING PROBLEMS OF FLEXIBLE BEAMS

作　　者：刘小靖[1] 王记增[1] 周又和[1] 

机构地区：[1]西部灾害与环境力学教育部重点实验室,兰州大学土木工程与力学学院力学与工程科学系,甘肃730000

出　　处：《固体力学学报》2013年第S1期159-165,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11032006;11072094和11121202);教育部新世纪优秀人才支撑计划项目(NCET-10-0445);教育部博士点基金项目(20100211110022);兰州大学中央高校基本科研业务费专项资金(lzujbky-2012-202)资助

摘　　要：本文介绍了一种采用广义泰勒级数展开技术进行边界延拓处理,适用于逼近定义在有限区间上的平方可积函数的,小波尺度基函数构造方法.基于此尺度基函数的小波逼近格式不但可以有效避免传统小波方法在求解微分方程时解在边界附近的跳跃或抖动问题,同时还可以自动满足微分方程的任意齐次边界条件.结合本文作者先前构造的广义小波高斯积分法,可以获得方程中任意非线性项的小波展开系数的显式表征格式.然后以此小波逼近格式为试函数,运用伽辽金方法定量分析了柔性梁的大挠度弯曲问题,通过将所得结果与其他方法所得结果比较,表明本文所介绍的小波算法具有更高的数值精度.进一步的研究结果表明该小波算法具有很好的计算效率和稳定性,并且还具有求解多解问题的能力.We develop a scheme of wavelet approximation for a function defined on a bounded interval by combining the so-called generalized-Gaussian-quadrature method developed earlier by the authors and the technique of boundary extension in terms of Taylor series expansion.When applying the proposed wavelet approximation to the solution of boundary value problems,the new scheme offers several unique properties,including that the expansion coefficients are just the function samplings at each nodal point,homogeneous boundary conditions can be automatically satisfied,and any undesired fluctuating errors to the numerical solution near the boundary points can be eliminated.These properties make the nonlinear terms of the unknown function in the equations to be expanded explicitly,and enable us to eventually get a stable,high accuracy and efficient numerical method for the treatment of large deflection problems of structural mechanics.Examples on large-deflection bending of beams have been studied to justify the proposed method.

关 键 词：柔性梁 大挠度弯曲 小波伽辽金方法 多解问题 

分 类 号：O342[理学—固体力学] O174.2[理学—力学]