阶梯柱屈曲的改进Fourier级数分析

该文对阶梯柱的弹性屈曲问题进行了研究.首先基于改进Fourier级数法采用局部坐标逐段建立阶梯柱的位移函数表达式,然后由带约束的势能变分原理得到含屈曲荷载的线性方程组,利用线性方程组有非零解的条件把问题转化为矩阵特征值问题得到临界载荷,最后讨论方法中的参数取值,并把结果与已有文献和有限元的结果比较,从而验证方法的精度.所提模型在阶梯柱的两端和变截面处引入横向弹簧和旋转弹簧,通过改变弹簧的刚度值模拟不同的边界.所提方法在工程设计中能比较精确地确定各种弹性边界条件下阶梯柱的临界载荷.

Buckling Analysis of Stepped Columns Based on the Improved Fourier Series Method

The elastic buckling of stepped columns with variable cross sections was studied. Firstly, based on the improved Fourier series method, the displacement function of the column was established in the local coordinate system, then the linear equations for buckling loads were obtained with the constrained variational principle of potential energy. The problem was transformed into a matrix eigenvalue problem and the buckling load was obtained from solution of the matrix eigenvalues. Finally, the parameter values in the method were discussed through numerical examples, and the obtained results were compared with the finite element results and previous literature results so as to verify the accuracy of the method. In the presented model the translational and rotational springs were arranged at the 2 ends and the setback cross sections. The method can determine the buckling loads of stepped columns with various elastic boundary conditions accurately in engineering design.