考虑弯曲位移影响的解析型压杆单元构造

Analytical element for compressive bar considering flexural displacement

利用解析形函数构造了压杆单元,可用于求解压杆稳定问题.基于考虑二阶效应影响的压杆微分平衡方程,得到以节点位移表示的压杆位移形函数,利用能量法和解析形函数得到压杆单元势能泛函表达式.对压杆单元势能泛函变分,确定了考虑弯曲位移影响的压杆单元弹性刚度矩阵和几何刚度矩阵.为检验解析型压杆单元的精度,将提出的方法与插值形函数法和直接刚度法进行对比,结果表明:提出的解析型压杆单元具有较高的计算精度和效率.

The element for compressive bar was constructed to deal with the stability problems by analytical shape function. Considering the second order effect,the equilibrium differential governing equation of compressive bar was established,and the corresponding displacement shape functions were derived and expressed by node displacement. The potential energy functional expression for compressive bar element was developed by potential energy principle and analytical shape function. Considering the effect of flexural displacement,the elastic and geometrical stiffness matrices were proposed through the variation of total potential energy. To verify the precision of the proposed element,the numerical comparisons were conducted among the interpolation shape function method,the direct stiffness method and the analytical shape function method. The results show that the proposed element has high calculation precision and efficiency.