考虑剪切变形效果的薄壁结构三维动力计算

3-D dynamic computation of thin-walled structures with considering the effects of shear deformations

为了分析考虑剪切变形效果的薄壁结构三维振动响应,本文推导剪切变形梁柱单元动力刚度矩阵,首先列出一般形式下薄壁梁柱的势能方程,得到位移与力之间的转换方程;接着,推导力与变形的关系,并采用变分原理,从势能方程中得到动力方程;然后,构造14个位移参数的变量来对高阶的动力方程进行降阶与求解,从而得到精确的位移函数表达式及动力刚度矩阵。数值算例的检验结果表明,这套程序计算所得到的结果与NASTRAN计算结果相一致,说明这一结果具有较好的通用性,它提供给薄壁结构振动计算一个较为实用的工具。

For analysis of spatial vibration of thin-walled space frame members with considering the effects of shear deformations,this article derives dynamic stiffness matrix for a shear-deformable beam-column element. First, total potential energy of thin-walled beam-columns in the general form is presented, and the transformation equations between displacements and forces are dervied. Next, force-deformation relations are obtained and the dynamic equations are dervied from the total potential energy by invoking the variation principle. And then, the higher order differential equations may be transformed into the first order differential equations by choosing a variable which contains 14 displacement parameters, the explicit expressions for displacement parameters and exact dynamic stiffness matrix are thus determined. The numerical example indicates that the results gotten by this program are consistent to those gotten by NASTRAN, so it＇s a general formulation and provides an applied tool for the vibration computation of thin-walled structures.