Narrow Results

In the present study, the bending collapse of an elastoplastic cylindrical tube subjected to static pure bending is investigated using the finite element method (FEM). The moment of the elastoplastic cylindrical tube is controlled by the flattening rate of the tube cross-section. For a long tube, the flattening rate can be expressed in terms of the axial and circumferential stresses that, in turn, depend on the material and geometrical properties and the curvature of the tube. On the other hand, for a short tube, the boundary condition of the fixed walls prevents the flattening rate. In order to account for the length effect of tubes, we propose a new method in which flattening is considered as a deflection problem of a fixed curved beam. The proposed method was able to predict the change in the flattening rate as the curvature was increased. A rational prediction method is proposed for estimating the maximum bending moment of cylindrical tubes that accounts for the length effect. Its validity is demonstrated by comparing it predictions with numerical results obtained using the finite element method.

Symmetric and anti-symmetric trapped modes in a cylindrical tube with a segment of higher density are studied. The problem is reduced to an eigenvalue problem of the spatial Helmholtz equation subject to vanishing Dirichlet boundary condition in the cylindrical coordinate system. Through the domain decomposition method and matching technique, multiple frequency parameters are determined by solving the characteristic equation, and the corresponding n-fold periodic trapped modes can be constructed. It is found that in addition to the fundamental mode, the second- and higher-order trapped modes exist, which depend on the density ratio and length of the inhomogeneity. The local inhomogeneity leads to a decrease of the cutoff frequencies of the homogeneous tube and the corresponding vibration mode is localized near the inhomogeneous segment.