Refined Beam Models for Static and Dynamic Analysis of Wings and Rotor Blades

Abstract

This paper presents the finite element analysis of slender thin-walled bodies by means of different finite element models. The beam formulation is given in the framework of the Carrera Unified 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 1D generalized displacement variables. The refined kinematic models are based on Taylor-type polynomials. The finite 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, refined models are then introduced to evaluate non-classical effects. Aircraft wing and wind turbine blade models are analyzed. Static and dynamic analyses are conducted. It has mainly been concluded that the enhanced refined beam element, which has been formulated via CUF, is able to detect the so-called shell-like mechanical behaviors, that is, shell-like results can be obtained using higher-order beam elements. The shell-like capabilities include the detection of the local displacement field induced by a concentrated load, and natural modes characterized by the presence of waves along the cross-section contour.