tailieunhanh - Elastoplastic stability of thin rectangular plates under complex and impure loading

This paper deals with investigation of the elastoplastic stability of thin rectangular plates. The plate considered herein is subjected to the biaxial compressive forces which are assumed to be linearly distributed along every its edge. | Vietnam Journal of Mechanics, NCST of Vol. 23, 2001, No4 (205 - 215) ELASTOPLASTIC STABILITY OF THIN RECTANGULAR PLATES UNDER COMPLEX AND IMPURE LOADING Vu CONG HAM Le Quy don Technical University ABSTRACT. This paper deals with investigation of the elastoplastic stability of thin rectangular plates. The plate considered herein is subjected to the biaxial compressive forces which are assumed to be linearly distributed along every its edge. The governing equations of the problem are formulated with applying the elastoplastic process theory whereas Bubnov - Galerkin method is used to calculate the critical forces. In the paper the author proposes a new method to determine the elements of the matrix concerned with the instability moment of the structure and applies the Gaussian quadric method for integral calculation. Some results of numerical calculations are also presented in the paper. · 1. Introduction Let 's consider a thin rectangular plate which has the biaxial dimensions a, b and the thickness h. A coordinate orthogonal system Oxyz (or Ox 1 x 2 x 3 in tensor notations) is attached to the plate so that the plane Ox y coincides with the middle surface and the four edges can be mathematically described as x = 0, y == 0, x =a, y = b, respectively. In [2 , 3, 4, 5] . the so called pure loaded state is considered. According to this loaded state, the plate is subjected to one or any combination of biaxial compressive forces p, q and shear force T (figure 1) . These external forces are assumed to act in the middle surface and to be evenly distributed along every edge of the plate. Because of this, the prebuckling stress-strain state is pure at any point in the plate 205 This paper is concerned with the impure loading. The plate in the considered case is subjected to biaxial compressive forces p, q which are also assumed to act in the middle surface, but to be unevenly distributed along each edge, respectively. Because of mathematical difficulties, the .