Dynamic and Post-buckling Analysis of Structures Like-Shell Using a Quadrilateral Shell Element with In-plane Drilling Rotational Degree of Freedom and a Conservative Implicit Time Integration Scheme

摘要

In this work, post-buckling problems of structures like shell are investigated using an implicit conservative time integration dynamic scheme. We have proposed the use of a four nodded quadrilateral flat shell element, with the drilling rotation degree of freedom (D. Boutagouga., A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions, Int. J. Numer. Meth. Eng. 2017; 110:573-600) and based upon the updated Lagrangian formulation. An implicit conservative scheme (K.J, Bathe., G, Noh., Insight into an implicit time integration scheme for structural dynamics. Comput. Struct. 2012; 98-99: 1-6) is chosen to obtain the solution to the nonlinear dynamic behaviour and geometric nonlinear post-buckling response. Several numerical simulations are considered in the aim to investigate the ability of the considered time integration scheme to deal with unstable branches after the limit point in non-linear post-buckling response of shell structures with no prerequisite structural damping, though it is required when using conventional time integration schemes. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme combined with the quadrilateral shell element with drilling rotation.