铁摩辛柯梁弯曲问题的精细积分法  

PRECISE INTEGRATION METHOD FOR THE BENDING PROBLEMS OF TIMOLSHENKO BEAMS

作　　者：胡启平[1] 孙良鑫[1] 高洪俊[1] 

机构地区：[1]河北工程大学土木学院,邯郸056038

出　　处：《工业建筑》2007年第z1期268-270,共3页Industrial Construction

基　　金：河北省自然科学基金资助项目(E2006000630);河北省教育厅自然科学基金资助项目(2002147)

摘　　要：Timoshenko梁弯曲问题的哈密顿对偶方程,是关于梁截面上的广义力和广义位移的一阶常微分方程组,可与现代控制理论的一些问题相比拟。由于系统矩阵具有辛矩阵的特性,数值计算具有良好的稳定性,可将Timoshenko梁弯曲问题的两端边值问题转化成初值问题,用精细积分法求得高精度的数值解。算例计算结果表明,本方法具有较高的精度和适用性,并可方便地用于变截面梁的计算。Hamilton dual equations of Timoshenko beams bending problems are the first-order ordinary differential equations on generalized forces and generalized displacements of beam sections,which can be assimilate some problems in modern control-theory.Numerical calculation has good stability because the system matrix has characteristics of the symplectic matrix,and the double end boundary value problems of Timoshenko beams bending problems may be transformed to initial value problems,then numerical solutions with high accuracy are often obtained with the precise integration method.The results of the example show that the method has higher precision and applicability.Moreover,it can be applied conveniently to calculating problem of non-uniform beams.

关 键 词：TIMOSHENKO梁 对偶求解体系 哈密顿对偶方程 精细积分法 变截面 

分 类 号：TU311[建筑科学—结构工程]