An element nodal force-based large increment method for elastoplasticity

This paper presents a new method for establishing the basic equations in the novel force-based large increment method (LIM) for continuum elastoplastic problems. In LIM, unlike traditional displacement methods, the (generalised) elemental force variables are adopted as system unknowns. The equilibrium equations can then be obtained directly at every nodal degree of freedom without physical equations (i.e., constitutive equations) involved. The generalised inverse of the non-square system of equations is employed to obtain the set of solutions of the non-square matrix equations directly. A conjugate gradient procedure is then used to find the correct solution from this set of solutions by optimising the compatibility of the solution based on the fact that the correct solution should also satisfy the constitutive equations and the compatibility equations. In this paper, the generalised elemental force variables are defined based on the element nodal forces. The LIM framework is therefore successfully applied to elements based on this definition. The efficiency and accuracy of the LIM are illustrated with a few benchmark problems and the results are compared with the analytical solution and the conventional displacement-based finite element method.