Rotation-free finite element for the non-linear analysis of beams and axisymmetric shells

In this paper a finite element for the non-linear analysis of two-dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions (no transverse shear strains). The main feature of the element is that it has no rotational degrees of freedom. Curvatures are computed using geometrical information from the patch of three elements formed by the main element and the two neighbor (adjacent) elements. Special attention is devoted to non-smooth geometries and branching shells. An elastic–plastic material law is considered. Large strains are treated using a logarithmic strain measure and a through-the-thickness numerical integration of the constitutive equations. Several examples are presented including linear problems to study convergence properties, and non-linear problems for both elastic and elastic–plastic materials and large strains.