A Beam Formulation with Shell Capabilities

Re ned beam theories suitable for aerospace structures are presented in this paper. These theories have shell capabilities and permit the analysis of thin walled structures, such as wings and helicopter blades. The formulation is given in the framework of the Carrera Uni ed Formulation, CUF, which considers the order of the theory, N , as a free parameter of the analysis. N is the order of the 1D displacement expansion. The displacement components are, in fact, expanded in terms of the cross-section coordinates, (x, z), by using a set of 1-D generalized displacement variables. The re ned kinematic models are based on Taylor-type polynomials. The nite element formulation is exploited in order to be able to face arbitrary cross-section geometries. FE's matrices are obtained in terms of a few fundamental nuclei which are formally independent of both N and the number of element nodes. A cubic (4 nodes) approximation along the beam axis, (y), is used. Structural analyses are conducted starting from classical beam theories, re ned models are then introduced to evaluate non-classical e ects. Di erent cross-section geometries, loading cases and boundary conditions are considered. It is mainly concluded that re ned models are mandatory to properly detect shell-like mechanical behaviors. CUF hierarchical capabilities o er a powerful systematic procedure to implement higher-order beam theories with no constraints on N .