矩形梁受分布荷载的辛解答  

SYMPLECTIC SOLUTION OF A RECTANGULAR BEAM SUBJECTED TO DISTRIBUTED LOAD

作　　者：朱炳麒[1] 周建方[1] 卓家寿[2] 

机构地区：[1]河海大学机电工程学院,常州213022 [2]河海大学土木工程学院,南京210098

出　　处：《力学与实践》2007年第3期15-19,共5页Mechanics in Engineering

基　　金：教育部高等学校博士学科点专项科研基金(20010294002)

摘　　要：在弹性力学平面直角坐标辛体系中,采用分离变量法,放弃齐次边界条件,得到了矩形梁侧边受幂函数形式分布荷载问题的辛解答,给出了这类问题在辛体系中的一般解法,分别对矩形梁受法向和切向分布荷载的问题进行了求解,显示了此方法的有效性．辛解法采用对偶的二类变量进行求解,可同时给出位移和应力;由于辛解法能较好地处理各种边界条件,因此不仅能求解静定问题,也能直接求解静不定问题．In the symplectic system of plane elasticity in rectangular coordinates, by separating variables and abandoning the homogeneous boundary condition, the symplectic solution of a rectangular beam subjected to distributed load in a power function form is obtained. A general method for these problems is given in the symplectic system of elasticity. The rectangular beam subjected to normal or tangent load is considered. The results show that the method is effective. Displacements and stresses can be obtained directly with dual variables. By using the symplectic solution, various boundary conditions can be treated. Statically determinate problems and statically indeterminate problems can be solved directly.

关 键 词：弹性力学辛体系 矩形梁 幂函数 分布荷载 辛解答 

分 类 号：O175.8[理学—数学]