ABSTRACT
This chapter presents details of the finite element formulation for isotropic, homogeneous 2D continua in Lagrangian description for finite deformation. These finite element formulations can be used to study axisymmetric deformation in bodies of revolution due to axisymmetric loads. The finite element formulations are derived in this chapter using principle of virtual work. These formulations are valid for solid matter undergoing finite deformation and finite rotations. Incremental form of the constitutive theory between second Piola-Kirchhoff stress and the Green's strain tensor yields symmetric tangent stiffness matrix when Newton's linear method is employed for obtaining solutions of non-linear algebraic equations. The finite element formulations that incorporate large deformation, finite rotations and finite strains and are based on second Piola-Kirchhoff stress and Green's strain tensor with incremental elastic constitutive equations are generally referred to as geometrically nonlinear finite element formulations in the published literature.
