Green’s-function-based-finite element analysis of fully plane anisotropic elastic bodies

In the paper, an anisotropic Green’s function based hybrid finite element was developed for solving fully plane anisotropic elastic materials. In the present hybrid element, the interior displacement and stress fields were approximated by the linear combination of anisotropic Green’s functions derived by Lekhnitskii formulation, the element frame fields were constructed by the interpolation of general shape functions widely used in the conventional finite element, and then they are linked by a new double-variable hybrid functional. Because the approximated interior fields exactly satisfied the governing equations related to anisotropic elasticity, all integrals in the present hybrid functional were performed along the element boundary and theoretically arbitrary hybrid polygonal element can be constructed. Finally, the present hybrid polygonal element with four edges was verified by making comparison of numerical results and exact solutions in a cantilever composite beam made with angled lamina.