Large strain elastic-plastic analysis of two-dimensional quasi-static structures

This paper discusses the formulation used in the development of an incremental finite element computer program designed for the nonlinear analysis of axisymmetric and two-dimensional quasi-static structures. A total Lagrangian description (initial configuration) is used for describing the equilibrium of the displaced position of the body and transformations to the Eulerian description (current position) are stablished. At each stage of loading, the strains are computed from the total displacements using the Green-Lagrange strain-displacement equations. The second Piola-Kirchoff stresses are calculated at each integration point within the finite elements and the necessary transformations are available to obtain Cauchy stresses. For an incremental analysis, the total load to be applied to the structure may be modeled as a series of load paths where each load path is divided up into several increments. Several solution algorithms are provided for integrating the structure from the beginning to the end of each load path. An equilibrium check is used at each stage of the analysis to insure that equilibrium is satisfied to a specified tolerance. No assumptions are made about the stress state at he beginning of a load path so that loading-unloading cycles are possible. Displacement dependent loads, including pressures, follower forces and radial body forces, are permitted in addition to thermal strains, fixed forces and specified displacements. Suitable constitutive formulations to describe the material nonlinearities may be developed using two different approaches and both are available in the present computer program