A solution by anisotropic expansion for a composite parallelepiped deformed into cylinder

摘要

We consider the application of complex variable method to elastic plane problems and investigate the nonlinear effect of the finite deformation of a compressible layered composite parallelepiped into a cylinder. By identifying a parameter of anisotropy we carry out pertinent expansion of dependent variables and provide a solution at the first level of approximation, which is the level that captures the nonlinearity of the problem. We obtain the nonlinear expressions for the normal force, tangential force and the bending moment, as higher order of the known case of small deformation solution for bending a plate. The effective moment is obtained and plotted against the bending angle, and this is compared to the case of linear theory.