Nine node and seven node thick shell elements with large displacements and rotations

In the present paper we discuss the total Lagrangian formulation for shell elements under large displacements and rotations to perform nonlinear geometrical analyses. This formulation is applied to nine node and seven node quadratic shell elements initially developed for small strain elasto-plastic analyses. The formulation we use is based on a three dimensional continuum approach in which we introduce a linear dependence of displacements with respect to thickness and a plane stress hypothesis. The measure of deformation we take is that of Green–Lagrange related to the second Piola–Kirchhoff tensor for the stresses by a linear material law. Linear buckling is treated as a limit case of the nonlinear geometrical analysis.