A CONVERGENCE ANALYSIS OF A P-VERSION FINITE-ELEMENT METHOD FOR ONE-DIMENSIONAL ELASTOPLASTICITY PROBLEM WITH CONSTITUTIVE LAWS BASED ON THE GAUGE FUNCTION-METHOD

In this paper, we will give a p-version finite element method for the one-dimensional nonlinear elastoplasticity problem. A family of admiss ible constitutive laws based on the so-called gauge function method is introduced first, and then a p-version semi-discretization scheme is presented. We show that the existence and uniqueness of the solution f or the semi-discrete problem can be guaranteed by using some special p roperties of the constitutive law. Finally, we show that as the polyno mial degree of the elements p --> infinity the solution of the semi-di screte problem will converge to the solution of the continuous problem . The p-version convergence analysis given here is only for one-dimens ional problems with a linear hardening constitutive law hypothesis. Ho wever, it also gives us a very useful idea for the study of the hp-ver sion finite element method for the one-dimensional problem with more g eneral constitutive laws or even two-dimensional problems.