三角函数剪切悬臂梁理论的位移边界条件

Displacement Boundary Conditions for the Trigonometric Shear Cantilever Beam Theory

工程上经常要计算在不同载荷作用下,狭矩形截面悬臂梁的挠度。在求解过程中,需要利用边界条件来确定位移场中的待定系数。该文应用三角函数剪切变形理论,讨论5种位移边界条件:两种传统位移边界条件,最小二乘法确定的位移边界条件和两种新的位移边界条件。在3种不同载荷作用下,求得悬臂梁中面的挠度公式,将得到的结果与有限元的数值计算结果进行比较分析,得出两种新的位移边界条件比传统位移边界条件得到的结果更加精确,在保证精度的前提下,比采用最小二乘法确定的位移边界条件计算更加简单,便于工程应用。

The paper presented the analytical results aimed at studying the deformations of cantilever beams based on the trigonometric shear theory. 5 different displacement boundary conditions were investigated. The first 2 conditions were the conventional simplified displacement boundary conditions,and the3 rd was determined with the least squares method. Besides,2 newsimplified boundary conditions were given in viewof the definition of the fixed end of cantilever beams. Compared with the solutions out of the finite element method,results from the 2 newboundary conditions were found to be much better than those from the conventional ones especially for short beams. The newly presented boundary conditions are more simple and easy to be coded by engineers than the least squares method.