The Finite Element Method in Problems of the Thin Shells Theory

This book focuses on the realization of curvilinear finite element models on the basis of vector approximation of the form function in problems of nonlinear deformation and stability of thin shells. A technique for constructing geometrically nonlinear finite element models of thin shells is proposed in the form of nonlinear algebraic equations system that take into account the curvilinearity of the shell elements and its shape imperfection as the initial perturbation of the solution. The book has two parts. The first part contains the original scheme of the finite element method on the basis of vector approximation of the form function in problems of linear deformation of thin shells. The proposed scheme is tested on a number of examples. The second part focuses on curvilinear finite element models of thin shells in a nonlinear vector formulation. This part exhibits a technique for constructing geometrically nonlinear finite element models of thin shells with imperfections of the shape. Stress and stability analysis of the thin free-form shells by used modification scheme of the finite element method are in this part.