Integrated FEM Formulation for Total/Updated-Lagrangian Method in Geometrically Nonlinear Problems.

Abstract

This paper presents a new integrated FEM formulation for geometrically nonlinear analyses. There have been two methods to solve the so-called large displacement problem, i.e., the total-Lagrangian method and the updated-Lagrangian method, and two types of FEM programming have been conventionally written. It is shown in the peresent paper that these two types of programming can be combined by the use of the covariant components of the incremental Green-Lagrange strain tensor and the contravariant components of the second Piola-Kirchhoff stress tensor in the convected coordinate system. The difference is only seen in the transformation of the constitutive tensor components. The stiffness matrices for the solid and shell elements by this formulation are illustrated in detail, and advantages and disadvantages of the proposed method are also discussed.