Developement of Plastic Collocation Method Extension of Plastic Node Method by Yukio Ueda, Member Masahiko Fujikubo, Member Masahiro Miura, Member Sum

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1 Developement of Plastic Collocation Method Extension of Plastic Node Method by Yukio Ueda, Member Masahiko Fujikubo, Member Masahiro Miura, Member Summary 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.

3 Fig. 1 PCM model

4 (a) Beam element (b) Discontinuous field (a) Plate bending element (b) Plane element Fig. 2 Mechanism of plastic hinge Fig. 3 Watanebe's hybrid stress models

5 (b) Plastic region Fig. 4 Morley's plate bending element Fig. 5 Modes of plasticity for Morley's element

6 Fig. 6 Hexahedron isoparametric element with eight nodes

8 (a) Plastic method region (b) Plastic section method (Mesh-I) (c) Plastic section method (Mesh-U) (b) Bazeley's element Fig. 7 Elastic-plastic analysis of a simply supported square plate under uniformly distrbuted lateral loads

9 (a) Thin plate (b) Thick plate Fig. 8 Elastic-plastic large deflection analysis of square plates under thrust

10 (a) Solid body under bi-axial (b) Solid body under torsional bending moments moment Fig. 9 Elastic-plastic behavior of prismatic solid body

11 (a) Model for analysis (b) Relationship between pressure and radial displacement of outer surface (c) Distributions of radial and circumferential stress components over transverse section Fig. 10 Elastic-plastic behavior of a long cylindrical tube with closed ends under internal pressure 4) Y. Ueda, T. Yao : The Plastic Node Method- A New Method of Plastic Analysis, Comput. Meths. Appl. Mech. Engrg., Vol. 34 (1982), DD A104. 6) Y. Ueda, K. Nakacho, M. Fujikubo : Application of the Plastic Node Method to the Thermal Elastic-plastic and Dynamic Problems, Comput. Meths. Appl. Mech. Engrg., (1985), 8) L. S. D. Morley : On the Constant Moment Plate Bending Element, J. Strain Anal., Vol. 8 (1971), pp

12 11) M. Robinson : A Comparison of Yield Surfaces for Thin Shells, Int. J. Mech. Sci., Vol. 13 (1971), pp. 345 ` ) R. Hill : The Mathematical Theory of Plasticity, Oxford Univ. Press, 1950, pp. 106 ` 125.

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