复合载荷下波纹管横向非线性弯曲摄动有限元法

采用新的小参数、将摄动法和有限元法相结合,研究了复合载荷作用下波纹管横向非线性弯曲的位移和应力分布。小参数为结构环向应变的均方根。将节点位移摄动展开,并以复合载荷的等效节点载荷为参考载荷,将其公共系数1摄动展开。由此划分载荷的级别、建立各级载荷和相应位移的关系,避免了常规的迭代运算。算例为一考虑自重的U型波纹管在注满水时的横向非线性弯曲问题。计算表明,波纹管的挠度和膜应力有非常显著的非线性效应;当最大挠度与壁厚之比达到5.1后本法将失效。本法在摄动小参数的选取和复合载荷的处理上有特色,能解决较大的挠度问题。

FINITE ELEMENT PERTURBATION METHOD FOR NONLINEAR ANALYSIS OF BELLOWS UNDER LATERAL COMPOUND LOAD

Nonlinear deflection and the stress distribution of the bellows under lateral compound load are studied by the finite element perturbation method. The root-mean-square value of the circumferential strains of the structure is defined as a small parameter of the perturbation. The nodal displacement vector is directly expanded by the parameter but the equivalent nodal force vector is treated as a reference load with a common coefficient that is equal to unity and expanded by the parameter. In this way, the load is graded and the relations between the graded load and the corresponding displacement are established, therefore the routine iteration approach to the nonlinear problem is avoided. The U-shaped bellows fully filled with water under the material weight load is taken as an example. The result shows that the nonlinear effects are very strong on the deflection and the membrane stresses of the structure, and the method is effective when the ratio of the maximum deflection to the wall thickness is not greater than five. It is believed that the method can be extended to other structures.