移动载荷作用下多跨超静定梁内力及变形计算的奇异函数法  

Singular function method of calculating internal forces and deformation for multi-span statically indeterminate beam under moving loads

作　　者：卓士创[1] 蔡瑜玮[2] 李顺才[2] 

机构地区：[1]徐州师范大学物理与电子工程学院,江苏徐州221116 [2]徐州师范大学机电工程学院,江苏徐州221116

出　　处：《徐州师范大学学报（自然科学版）》2010年第3期55-59,共5页Journal of Xuzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(50974107)

摘　　要：多跨梁在移动载荷作用下的强度、变形计算及其动态响应问题,在道路、桥梁及机械设计中广受重视.经典的力学方法对多跨超静定梁在移动载荷作用下的内力及变形的求解十分繁琐.采用奇异函数法,可以简化问题的求解.用奇异函数不需分段即可表示整梁的弯矩方程和挠度方程,输入到软件Mathcad中,通过数值计算和图形处理的功能模块,可以快速绘制任意横截面的内力及变形随移动载荷位置的变化曲线,进而确定指定截面的最不利荷载位置及全梁的最大弯矩及其截面位置.多跨梁在不同几何尺寸或不同大小的载荷作用下的内力图及变形图,只需在Mathcad软件中修改相应的参数即可得到.The strength,deformation and dynamic response of multi-span beam under the moving loads have been paid much attention in the design of roads,bridges and machines. It is very tedious to use the classical mechanical method for solving the internal force and deformation of the multi-span statically indeterminate beam under moving loads. The singular functions method can simplify solving this problem. The equations of bending moment and deflection can be expressed by singular functions for the whole beam,and written into the Mathcad software. Through its function modules of numerical computing and graphics processing,we can quickly draw the curves of the internal force and deformation with the position variation of the moving loads for arbitrary cross-section,and thus get the most unfavorable load position on the designated section,and the location of maximum bending moment and the section in the whole beam. For the multi-span beams with the different geometric sizes or different load levels,the internal forces and deformation diagrams can be obtained only by modifying the corresponding parameters in Mathcad.

关 键 词：多跨梁 移动载荷 奇异函数法 MATHCAD 弯矩图 挠度 

分 类 号：O342[理学—固体力学]