NEW NONLINEAR HIGHER ORDER SHEAR DEFORMATION SHELL ELEMENT FOR METAL FORMING AND CRASHWORTHINESS ANALYSIS: PART I. FORMULATION AND FINITE ELEMENT EQUATIONS

This work presents the finite element formulation of a higher order shear deformation shell element for nonlinear dynamic analysis with explicit time integration scheme. A corotational approach is combined with the velocity strain equations of a general third order theory in the formulation of a four- noded quadrilateral element with selectively reduced integration. A bilinear isoparametric formulation is utilized in the shell plane resulting in 9 degrees of freedom per node. The formulation requires C0 continuity for the nodal variables. The finite element implementation of the new element in a general explicit finite element code is described in details, including boundary conditions and nodal mass calculation. A simple formula for the explicit time integration critical time step of the higher order element is developed. The described element is capable of correctly representing the through thickness distribution of the transverse shear, which makes it suitable for composite and sandwich shells analysis. In addition, the developed shell can be used for better representation of plastic flow through thickness in isotropic materials. It has been added to the element library of the nonlinear explicit finite element code DYNA3D. Its performance has been evaluated through a series of standard shell verification test problems, which show great promise for many applications. The results are presented in Part II of the present work.