Abstract
A methodology initially proposed for authomatic mesh generation of triangular and quadrilateral finite element discretizations in linear two-dimension problems is now extended to material nonlinear analysis. The technique, which is based on a h-adaptive process, is capable of achieving a specified discretization density using a powerful mesh generator. The element solutions at the nodes are obtained through a general stress recovery procedure employing an a posteriori error estimator. The constitutive equation is approached in the formulation using a flow theory to describe the elasto-plastic material behavior. In this study the von Mises condition is employed for the state of multiaxial stress corresponding to the start of plastic flow, the normality condition furnishes a flow rule in the plastic strain increments subsequent to yielding and the kinematic hardening is assumed as hardening rule. The adaptive procedure is based on the complete mesh regeneration and specific mesh requirements (boundary conditions, geometry definitions and space node function), and aims for an optimality condition with the least number of elements that yields an uniform error distribution in all elements. In the stress recovery process the nodal values are assumed to belong to a polinomial expansion defined over patches of elements adjoining a particular assembly node considered. The nodal point parameters, at each element, are obtained using a least square fit of superconvergent sampling points existing in the patch. The material uniaxial elasto-plastic constitutive behavior is represented using overlays, defined over small strain increments, allowing for the representation of the material kinematic hardening behavior beyond the classical bilinear relation. The procedure error estimation is obtained from differences between the post-processed stress gradients and those from the finite element solutions. The energy error norm associated with stress field diferences and the finite element strain energy gives an effective error estimate, used for comparison with the process tolerance. Evaluation of the proposed technique is presented through two numerical sampling analyses that illustrate its applicability in the improvement of the solution accurance of general two-dimension finite element model solutions.
