The Buckling Study Of U-Shaped Bellow Under Torsion Loading

The thesis numerically analyzes the intensity and the buckling of U-shaped bellows under torsion loading.The stress and displacement distributions of the bellows under torsion loading are investigated by using both finite element method (FEM) and equivalent cylinder method. Results indicate that under torsion loading, as the number of convolutions increases, the shear stresses in the bellows keep constant, but the torsion deformation is increased gradually. And both equivalent cylinder method and FEM give the same results for the shear stresses. As a result, for the calculation of shear stresses, the equivalent cylinder method is an effective way.FEM analysis shows that under torsion loadings, two different buckling modes can occur, namely in-plane squirm and column squirm. Increasing the number of convolutions, the buckling modes would changefrom in-plane squirm to column squirm and the critical buckling loading would decrease gradually. The bellow with small convolution height is apt to buckle in in-plane squirm mode, and the bellow with small convolution pitch is apt to buckle in column squirm mode.The thesis has also performed nonlinear buckling of U-Shaped bellow under torsion loading. The results indicate that when the U-shape bellow under torsion loading is going to buckles, the shear stresses Sxy and Syz nearly keep unchanged, and nevertheless, the normal stresses Sx, Sz and the shear stresses Szx increase speedily until the buckling have occurred. Comparing the nonlinear buckling analysis with the linear buckling analysis, it is found that for the in-plane squirm, it is unsafe to replace the nonlinear buckling analysis by the linear buckling analysis, while for the column squirm, it is safe in some degree to do so.