A 4-node thin shell element based on co-rotational for laminated composite structures

Abstract

The finite formulation of the 4-node thin shell element based on Co-rotational (CR) and Timoshenko`s theory was presented for the analysis of laminated composite structures. Based on the Timoshenko`s theory the present thin shell element avoids shear locking behavior, and a bilinear in-plane displacement field is introduced for the coupling of in-plane and bending actions, and such element performs simple formulation and highly efficienct. A highly efficient CR formulation was also established to define the motion of the element with large displacement. The characteristics of the element are more pronounced when shells get thin, each node of the 4-node element has five degrees of freedom. An incremental iterative method based on the Newton Raphson method was used to solve the nonlinear equilibrium equations. A number of numerical examples were given to verify that the formula is computationally efficient and the results showed good agreement.