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.