求解超静定梁的分段独立一体化积分法  

A SUBSECTION INDEPENDENTLY SYSTEMATIC INTEGRAL METHOD FOR SOLVING PROBLEMS OF STATICALLY INDETERMINATE BEAM

作　　者：吴艳艳[1] 李银山[1] 魏剑伟[2] 李彤[3] 

机构地区：[1]河北工业大学工程力学系,天津300130 [2]太原理工大学土木工程系,太原030024 [3]华东理工大学机械与动力工程学院,上海200237

出　　处：《工程力学》2013年第B06期11-14,共4页Engineering Mechanics

基　　金：国家自然科学基金项目(10632040)

摘　　要：提出了一种求解复杂载荷作用下超静定梁弯曲变形问题的分段独立一体化积分法。分段独立一体化积分法首先将梁进行分段,独立建立具有4阶导数的挠曲线近似微分方程,然后分段独立积分4次,得到挠度的通解。根据边界条件和连续性条件,确定积分常数,得到剪力、弯矩、转角和挠度的解析函数,同时绘出剪力图、弯矩图、转角图和挠度图。工程实例表明,分段独立一体化积分法建立方程简单,计算编程程式化,利用计算机求解速度快,与有限元法相比其优点是可以得到精确的解析解。A subsection independently systematic integral method （SISIM for short） is proposed for solving bending deformation problem of statically indeterminate beam under complex load. In SISIM, the beam is separated into segments firstly, and then the approximate forth-order differential deflection equations are established independently. Finally the general solutions of beam deflection are obtained by forth-fold integration for each segment. Integral constants are determined by imposing boundary conditions and continuity conditions, thus analytical functions of shear force, bending moment, angle of rotation and deflection are obtained, as well as the shear force diagram, bending moment diagram, angle of rotation diagram and deflection diagram. The engineering example shows that setting equations by SISIM is simple to apply and convenient to be fulfilled by computer programming. Compared with the finite element method, the advantage of SISIM is that exact analytical solution can be obtained.

关 键 词：超静定梁 快速解析法 分段独立积分 一体化解法 复杂载荷 

分 类 号：TU311[建筑科学—结构工程]