Nonlinear Transient Response of Isotropic and Composite Structures With Variable Kinematic Beam and Plate Finite Elements

Abstract

The present research deals with the evaluation of nonlinear transient responses of several isotropic and composite structures with variable kinematic one-dimensional (1D) beam and two-dimensional (2D) plate finite elements with different initial deflection configurations. The aim of current investigations is to show the effect of large amplitudes and the need to adopt an accurate model to capture the correct solution. Particular attention is focused on detailed stress state distribution over time and in the thickness direction. The proposed nonlinear approach is formulated in the framework of the well-established Carrera Unified Formulation (CUF). The formalism enables one to consider the three-dimensional (3D) form of displacement-strain relations and constitutive law. In detail, different geometrical nonlinear strains from the full Green-Lagrange (GL) to the classical von Kármán (vK) models are automatically and opportunely obtained by adopting the CUF due to its intrinsic scalable nature. The Hilber-Hughes-Taylor (HHT)-α algorithm and the iterative Newton-Raphson method are employed to solve the geometrical nonlinear equations derived in a total Lagrangian domain. Both Lagrange (LE) and Taylor (TE) expansions are considered for developing the various kinematic models. The solutions are compared with results found in available literature or obtained using the commercial code Abaqus. The results demonstrated the validity of the proposed formulation and the need to adopt a full Green-Lagrange model in order to describe the highly nonlinear dynamic response and an Layerwise (LW) approach to accurately evaluate the stress distribution.