Mixed Finite Element Solution of Quasi-Static Problems of Viscoplastic Plates
The paper is concerned with the numerical analysis of rigid, viscoplastic and elastic viscoplastic plates subjected to static loading. The small deflection theory of thin plates is employed. The constitutive equations of viscoplasticity are taken in the form proposed by Perzyna. A numerical solution scheme is formulated by using the mixed element method in which the nodal values of bending moments and of deflection are the unknown discrete parameters to be determined. Both the triangular elements presented by Hellan and Herrmann and the rectangular element proposed by Bäcklund have been used. Two methods have been considered for solving the resulting system of ordinary first-order differential equations with nonlinear coefficients. Sample problems which have been solved include simply supported circular plates subjected to uniform load and to concentrated load at the the center and simply-supported rectangular plate under uniform load. The viscoplastic algorithm has also been used for the determination of limit loads of circular and rectangular rigid plastic plates.
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