曲杆有限元与拱的临界载荷算法

从初应力位形上附加变形的场论出发,提出弹性屈曲问题的控制方程和变分原理的普遍形式;在这个理论框架下,通过降维处理,导出平面拱弹性屈曲问题求解临界载荷的变分方程、控制方程以及相应的线性齐次微分方程的特征值问题;进一步放弃平截面假设,考虑剪切变形,给出曲杆截面含6个自由度的一维有限元法算法.推导过程和计算结果表明,该理论体系导出曲杆有限元方程准确,易于数值实施,计算结果更符合实际情况.

Elastic Buckling and Critical Load of an Pre- stressing Arch

According to the field theory of additional deformation on pre - stressed configuration , in the paper , the ordinary expression of the governing equation and variational equation of elastic buckling are brought forward . Under the theory system, through lowering dimensions, the governing equation and variational equation for the critical condition solution of elastic buckling of a plane arch are deduced, and the eigenvalues problem of the linear homogeneous differential equations corresponding to the equations are concluded While Abandoning the plane assumption and considering shearing deformation, the linear finite element method arithmetic of bending bar's cross section containing six degree of freedom is given. The process of derivation and calculational results show that, under this system info, the finite element equations of bending bar deduced are accurate and easy to be used to numeric calculations, and the conclusion achieved is more practical.