Manuel Ritto-Corrêa

Work-conjugacy between rotation-dependent moments and finite rotations

In this paper we investigate the work-conjugacy between rotation-dependent moments and finite rotation measures. The methodology adopted consists of writing all the relevant quantities in terms of the rotation vector, using expressions that remain exact in the finite rotation range. Through this procedure, we show how (i) to identify work-conjugate (rotation-dependent) moments and rotation measures, (ii) to derive a necessary condition for moment conservativeness and (iii) to obtain the general form of an isotropic conservative rotation-dependent moment. Several moment and finite rotation definitions that have been used in the past are investigated and, in particular, it is shown that the various existing definitions for the so-called semi-tangential moments are distinct in the finite rotation range and that not all of them are conservative. The tangent operator symmetry is discussed in the context of finite element analysis of conservative systems with rotational degrees of freedom, adopting either an additive or a multiplicative update.

On the Interpolation of Rotations and Rigid-Body Motions in Nonlinear Beam Finite Elements

The formulation of 3D geometrically exact beam finite elements relies heavily on the interpolation scheme used for the unidimensional variables describing the rotations or the rigid-body motions of the beam cross-sections. Since these rotations and positions belong to the non-commutative Lie groups SO(3) and SE(3), they are not easily amenable to a direct discretisation.

A Large Displacement and Finite Rotation Thin-Walled Beam Finite Element Formulation

In this paper, one presents, implements and validates a total Lagrangian beam finite element formulation capable of handling large displacements and finite rotations, as well as cross-section in-plane (distortion and local bending) and out-of-plane (warping) deformations. This formulation can be viewed as a generalisation of the well-known Reissner-Simo beam theory that includes warping/transverse bending deformation modes and in which the member walls can undergo in-plane finite relative rotations. When compared with a shell finite element discretisation, the proposed beam formulation has the distinct advantage of drastically reducing the number of degrees-of-freedom required to achieve equally accurate results. Initially, the kinematical description of the member is addressed, devoting special attention to the assessment of the transverse plate bending effects associated with cross-section distortion. Next, the equilibrium equations and the corresponding symmetric tangent operator are obtained, by assuming an additive update of the rotational parameters. In order to illustrate the application, provide validation and show the capabilities of the proposed formulation, several numerical results are presented, discussed and compared with values yielded by large displacement shell finite element analyses (see Fig. 1) - one obtains a good correlation in all cases, which clearly demonstrates the vast potential of the proposed formulation. Open image in new window Figure 1 Beam deformed configurations yielded by the (a) proposed beam formulation and (b) shell element model