Shell elements as a coupling of plate and "drill" elements

In this paper a discretization of shell structures by means of flat elements is considered. The curved surface of the shell is approximated with a polyhedric surface; on each plane a finite element decomposition is introduced. Since on each element the "in plane" and bending forces cause independent deformations, a shell element is obtained by coupling in a suitable way a membrane element with a plate bending element. In this work membrane elements with drilling degrees of freedom are considered. In this way the shell elements that we shall construct will possess, in a natural way, also the degree of freedom related to the rotation along the vertical direction. This fact permits us to avoid the difficulties of programming arising from the use of classical membrane elements in which the rotational degree of freedom is absent. The numerical results performed with these new shell elements show their good convergence properties.