A computationally effective for mulationto finite rotations - Small strains description of beam elements

In the context of three-dimensional elastic frame structures analysis with small strains and in the presence of large rotations we present a computationally effective model for the Euler-Bernoulli beam element. Actually, kinematical and strain measures of the beam element are completely defined by referring to boundary nodal displacements and one finite rotation parameter solely. In particular, the director along axis of the beam is defined directly by nodal positions while directors along the principal axes of the cross-section are detected by referring to the related orthogonal plane and the used rotation parameter. The definition of local rotations, required for the evaluation of torque and flexural deformation components, is obtained by imposing rotational compatibility and equilibrium conditions across inter-element boundaries. The description of the finite three-dimensional rotations is well posed under widely applicable hypotheses. The analysis of complex spatial dome structures, where matrices with large dimension and bandwidth occur, now proves a remarkable reduction of the required arithmetical operations with respect to the classical approaches.