Incremental Nonlinear Finite Element Analysis of 3 node Co rotational Shell Element Based on U.L.

Abstract:

According to continuum mechanics and virtual work principle, incremental updated Lagrangian formulation (U.L.) was presented. The large displacement incremental stiffness matrix was considered in U.L., which was rectified to be symmetrical matrix. Based on U.L., three dimension general purpose three node triangular shell element was presented when the triangular shape function was employed, transverse shear stress was also considered. During the solution of incremental equilibrium equation, the pure nodal point incremental deformation was obtained when the rigid body rotation was removed from the nodal point incremental displacement by using co rotational procedure. Furthermore, by utilizing aforementioned theory, the nonlinear finite element program was developed. Several geometrically nonlinear numerical problems were presented to demonstrate the accuracy, effectiveness, and generality of the three dimensional three node shell element.