A geometrically nonlinear finite element formulation for shells using a particular linearization method

In this paper a particular linearization method is used to derive the updated Lagrangian finite element formulation for geometrically nonlinear analysis of shell structures. Derivation of the formulation is based on rewriting the Green–Lagrange strain and the second Piola–Kirchhoff stress as two second-order functions in terms of a through-the-thickness parameter. Substitution of these two functions into the equilibrium equation, from principle of virtual work, and then using a Taylor series expansion for the nonlinear term lead to a modified linearized incremental equation. In this procedure the stiffness matrices and the internal force vector are consistently derived following the linearization. The results are compared with those of other researchers and good agreements are observed. Advantages of the proposed approach are assessed and comparisons with available solutions are presented.