Transient Deformation of an Anisotropic Cylindrical Shell with Structural Features

Abstract

In this work, a new transient function of normal displacements is obtained in a thin elastic anisotropic cylindrical shell of constant thickness with structural features. Structural features form of two sequences in angular direction of weld spots or rivets. Structural features are mathematically described by point boundary conditions of rigid pinching or point boundary conditions of hinge support, accordingly. A load with time variable amplitude and impact boundaries influences on the outer surface of the shell along the normal. Such movement of the shell is considered in the cylindrical coordinate system as connected with the shell axis. Kirchhoff–Love hypothesis are confirmed as a shell model. The solution of this problem can be formed with the help of Green function method and lift compensation method. The required function of transient normal displacements is represented as the sum of integral operators of Green convolution for an infinite shell with functions of current transient load and compensating loads out of point boundary conditions. Compensating loads satisfying to boundary conditions can be found based on the solution of Volterra integral equations of the first kind with the difference kernel. Green function is such kernel. The system solution can be executed including preliminary discretization of compensating time loads. The convolution integrals can be taken numerically with the help of quadrature formula by the method of rectangles. The verification of the method is represented by comparing the solution of specific case with the known solution for a hinged isotropic cylindrical shell.