ENERGY PRINCIPLES AND FINITE ELEMENT INCREMENTAL FORMULATIONS FOR GEOMETRIC NONLINEAR PROBLEMS

Numerical methods for geometric nonlinear problems are core topics in computational mechanics. This paper generalizes and expands the measurements of large deformation, extablishing a unified derivation and expression of the energy principles and the finite element solution formulations for geometric nonlinear problems. The reference configurations of the deformable body are distinguished as unknown equilibrium configurations and known equilibrium configurations. The relationships among key principles and formulations are clarified, including the virtual displacement principle, the virtual power principle, and the incremental virtual displacement principle, the total Lagrangian formulation and the updated Lagrangian formulation, the solution strategies of linearization followed by element discretization and element discretization followed by linearization, and the constitutive equations with the total, incremental and rate variables.