AN INTEGRAL EQUATION ANALYSIS OF INELASTIC SHELLS

The boundary element method (BEM) has emerged as a powerful and accurate technique for obtaining numerical solutions to applied mechanics problems. However, applications of this method to shell theory have so far been limited. The primary reason for this has been the inavailability of Green's functions for general arbitrary shells.;This thesis presents an integral equation approach for the analysis and determination of numerical solutions for the deformation of shells of arbitrary shape subjected to arbitrary loading. The proposed mathematical model is derived by transformation of the three-dimensional equations from the Cartesian to the appropriate curvilinear coordinates of the shell. Besides transforming the 3-D equations to the shell midsurface, some assumptions are made in order to take advantage of the shell being thin. In particular, these assumptions are mainly concerned with the specification of the load on the edges and kinematic assumptions for the dependence of the displacements on the thickness coordinate of the shell.;Numerical implementation of the integral equation approach has been carried out for axisymmetric inelastic shells. The results for the linear elastic deformation of axisymmetric shells for several examples of toroidal and cylindrical shells have been compared against exact elasticity solutions in many cases. Inelastic results for cylindrical and toroidal shells under different load histories are also presented in this dissertation. The results for the inelastic cylindrical shell are compared against a semi-analytical solution based on Love-Kirchoff theory.