INTEGRATED FEM FORMULATION FOR TOTAL UPDATED-LAGRANGIAN METHOD IN GEOMETRICALLY NONLINEAR PROBLEMS

This paper presents a new integrated FEM formulation for geometrically nonlinear analyses. There have been two methods to solve the so-calle d large displacement problem, i.e., the total-Lagrangian method and th e updated-Lagrangian method, and two types of FEM programming have bee n conventionally written. It is shown in the present paper that these two types of programming can be combined by the use of the covariant c omponents of the incremental Green-Lagrange strain tensor and the cont ravariant components of the second Piola-Kirchhoff stress tensor in th e convected coordinate system. The difference is only seen in the tran sformation of the constitutive tensorial components. The stiffness mat rices for the solid and shell elements by this formulation are illustr ated in detail, and advantages and disadvantages of the proposed metho d are also discussed.