采用分段样条插值的半离散方法分析薄壁杆件

ANALYSIS OF THIN-WALLED MEMBERS BY A SEMI-DISCRETE METHOD USING SECTIONAL SPLINE FUNCTION

本文在文献[1]的基础上,提出一种基于势能原理的薄壁杆件的简化分析方法。该方法放弃了符拉索夫[2]关于沿杆横截面剪应变等于零或常数的假定,能很好地描述剪力滞后现象。杆横截面的纵向位移采用分段三次样条插值,通过变分原理,得到一组常微分方程及相应的自然边界条件。纵向位移沿杆长的分布,则可由解上述微分方程组得到一个闭合解。本方法适用于任意形式截面的薄壁杆件分析。算例表明了本方法的灵活性和精度及快速收敛的性能。

Based on the potential energy method, a semi-discrete method is presented in this paper. The method can save much computing time than the standard finite element method and even the finite strip method. By abandoning one of the Vlasov's assumption in analysis of thin-walled members, which assumption is that the shear strains along the central line of the cross section are zero or constant, the present method can show the shear lag effect well. In this paper, the longitudinal displacement along the cross section is interpolated by a new proposed sectional spline function. By using the variational principle, a group of ordinary differential equations and natural boundary conditions can be derived. By solving these equations an analytical solution for the longitudinal displacement along the member axis can be obtained. The present method is suitable for any shape of cross section thin-walled members. Some typical numerical examples in this paper demonstrate the versatility, efficiency, accuracy and convergency of the proposed method.