Abstract
Previously, the authors developed the plastic node method for elastic-plastic analyses of homogeneous continuum in any geometrical shape. In this method, using ordinary finite elements, plastification is examined only at the nodes. Regarding the yield conditions at the nodes as plastic potentials and applying the plastic flow theory, the elastic-plastic stiffness matrices can be derived without integration over the element. The successful applicability of this method has so far been verified.
By the way, the accuracy of the elastic-plastic behavior obtained by this method depends on that of the stresses in the elements and the yield conditions. Especially on the former one, it is generally agreed that the stresses evaluated at the Gaussian points or by means of averaging may be more relevant rather than nodal ones.
From this point of view, in this paper, the basic theory of the plastic node method is further extended so that plastification can be examined at any point in the element. In this sense, the authors name this extended theory the “plastic collocation method”. The theoretical background of this new method is also argued especially aiming at the mechanism of the plastic deformation in the element. Applying this plastic collocation method, several examples are analysed, and the effectiveness of this method is demonstrated.
