Nonlinear dynamic analyses of isotropic and composite structures using refined and unified one-dimensional finite elements

The present research work deals with the finite element analysis of the nonlinear dynamic behavior of isotropic and composite structures. The mathematical models of such structures are derived by exploiting the Carrera Unified Formulation (CUF). CUF represents a hierarchical formulation in which the order of the structural model is considered as an input of the analysis. Thus, no ad-hoc formulations are needed to achieve any refined generic model. According to CUF, any theory is degenerated into generalized kinematics adopting an arbitrary expansion of the generalized variables. In this work, Lagrange polynomials are employed as expansion functions. The nonlinear governing equations and the relative finite element arrays of the one-dimensional theories are formulated in terms of Fundamental Nuclei (FNs). Furthermore, geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method. Finally, the implicit time integration scheme employed to evaluate the nonlinear dynamic response is the Hilber-Hughes-Taylor (HHT)-α algorithm, which allows stabilising the time integration process under highly nonlinear effects. A preliminary analysis is performed to validate the proposed approach when compared with analytical and literature results. Subsequently, composite beams are considered, and stress distributions at highly nonlinear equilibrium conditions are evaluated. Finally, an application to a double-pendulum problem is proposed. The latter model is built in a multibody framework, joining the two different arms employing Lagrange multipliers. The results clearly show the reliability of the approach when dealing with nonlinear dynamics and evaluating the three-dimensional stress distribution. The analysis of the double-pendulum mechanism is promising for future multibody applications.