tailieunhanh - Báo cáo " ON THE STABILITY OF ELASTOPLASTIC THIN TRIANGULAR PLATES MADE IN COMPRESSIBLE MATERIAL "

The stability problem of thin triangular plates by the small elastoplastic deformation theory, was studied in [3]. Basing on the theory of elastoplastic processes, this problem again has been investigated in [4] with incompressible material. In this paper we continue to study the mentioned problem with compressible material. The relation for determining critical forces is established. In particular the explicit expression of the critical force for the linear hardening material is found. Some numerical calculations have been given and discussed. . | VNU. JOURNAL OF SCIENCE Mathematics - Physics. N04 - 2005 ON THE STABILITY OF ELASTOPLASTIC THIN TRIANGULAR PLATES MADE IN COMPRESSIBLE MATERIAL Dao Van Dung Chu Thi Tam Department of Mathematics College of Sciences VNU Abstract. The stability problem of thin triangular plates by the small elastoplastic deformation theory was studied in 3 . Basing on the theory of elastoplastic processes this problem again has been investigated in 4 with incompressible material. In this paper we continue to study the mentioned problem with compressible material. The relation for determining critical forces is established. In particular the explicit expression of the critical force for the linear hardening material is found. Some numerical calculations have been given and discussed. 1. Problem setting and fundamental stability equations Let s consider a isosceles right triangular thin plate with the right side a and thickness h. We choose a orthogonal coordinate system Oxyz so that the axis x and y coincide with two right sides of plate the axis z in direction of the normal to the middle surface. Assume that a material is compressible and the plate is sub jected to the compressible forces with the intensity uniformly distributed p p t at the sides x 0 y 0 and x y a where t - loading parameter. Moreover we suppose don t take into account the unloading in the plate. The problem is to have to find the critical value t t and respectively the critical load p p t which at that time t an instability of the structure appears. We use the crirerion of bifurcation of equilibrium state to investigate the proposed problem. . Pre-buckling state At any moment t in the plate there exists the plane stress state ơxx -p t -p ơyy -p t -p Cxy ơxz Cyz g .z 0- 1-1 So that 2 Ơ --- p 3 p u J ơ xx ayy ơxx ơyy p. The material is assumed to be compressible ơ 3K . So 3K K 9K E 3 1 - 2v E 2G 1 v where K is compressible coefficient of material. The components Typeset by AmS-TeX 14 On the .