Nonlinear weighted residual approach: application to laminated beams

A weighted residual formulation of equilibrium equations for nonlinear structural analysis is presented in material description. Starting from the strong form, the weak form is derived by means of a suitable choice of weighting functions. In order to get the tangent stiffness matrix of the finite element approximation, the weak form is first linearized and then discretized. This sequence is well suited when large displacement fields nonlinearly depend on degrees of freedom, which currently occurs in structures. The proposed formulation is applied to arbitrary large displacements of laminated plane beams including shear deformation. A discrete-layer approach with constant shear strain in each layer is assumed, leading to a zigzag behavior of the in-plane displacements through the whole thickness. Numerical applications to various problems show that the proposed model is quite accurate.