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Solution to the problem of the elastoplastic stability of thin rectangular plates in two cases of boundary condition

In this paper, the theory of the elastoplastic process is applied to derive the governing equations of stability problems of thin rectangular plates subjected to complex loading processes. The solution presented in the paper belongs to the two following cases of boundary condition. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 4 (30 - 40) SOLUTION TO THE PROBLEM OF THE ELASTOPLASTIC STABILITY OF THIN RECTANGULAR PLATES IN TWO CASES OF BOUNDARY CONDITION VU CoNG HAM Le Quy Don Technical University 1. Introduction In this paper, the theory of the elastoplastic process is applied to derive the governing equations of stability problems of thin rectangular plates subjected to complex loading processes. The solution presented in the paper belongs to the two following cases of boundary condition 1) The considered plate has all four edges clamped stiffly. 2) The considered plate has two opposite edges clamped stiffly while the two others are simply supported. The plates with four edges simply supported has been considered in [4]. 2. Governing equations of the problem Let's consider a rectangular plate with the thickness h and the lengths of the edges a, b. The coordinate system Oxyz is chosen such that the middle surface of the plate coincides with the plane Oxy and the four edges can be described by X = 0, X = a, y = 0, y = b. The external forces acting on the plate are biaxial compression forces of intensity p, q and shear force r. The upper forces are assumed to be increasingly and depend arbitrarily on a some parameter t (the loading parameter) p = p(t), q = q(t), r = r(t) so that the loading is really performed in a arbitrary process. It is important to determine the critical values t = t*, p* = p(t*), q* = q(t*), r* = r(t*) at which an instability appears. 30 An analysis of the stability problem is always made in two stages: the-buckling stage and the post-buckling stage. 1. Pre-buclding stage At any moment t there exists a plane stress state i:q the plate uu = -p, u22 = -q, = -r, u12 Uta = u2a = uaa = 0 (2.1) so that u= uu + u22 3 p+q ---3 (2.2) The components of deformation velocity are determined accordi¥g to the theory of elastoplastic process [1]. In case of process with average curvature, they