tailieunhanh - Buckling of nonlinear creep plates

In this paper the theory of pseudo-bifurcation points and a criterion of creep stability [1] are used to solve the problem on buckling of nonlinear creep plates according to Rabotnov's theory of hardening creep. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. U, lQQQ, No 4 (251- 256) BUCKLING OF NONLINEAR CREEP PLATES To VAN TAN, PRAM QUOC DOANH Hanoi University of Civil Engineering 1. Introduction Note that [1] the buckling of structures with immediate mechanical behaviour of the material (elastic, plastic) corresponding to the bifurcation points (of a stat e of strain or a process of strain) . However, the buckling of creep structures takes place after a determined period of time and corresponding to the pseudo-bifurcation points. In this paper the theory of pseudo-bifurcation points and a criterion of creep stability [1] are used to solve the problem on buckling of nonlinear creep plates according to Rabotnov's theory of hardening creep (2). 2. Stability of nonlinear creep plate Using Rabotnov's theory of hardening creep, we have . 3 . 1- p a: P.·,,-- -2 A_,nS 'J· · -- 0 ' v where •2 P 2 . (} . = 3Pi;P,;, u, P - stress intensity and creep strain intensity; Pt.; - creep strain components; s,; - components of stress deviator; E, A, a, n - mat erial constants determined by experiment. Assume that u9 e9. , W 0 'J 'J - stress, strain, deflection in the basic st ate. u 1;, et.;, W - stress, strain, deflection in the adjacent state such that the "stimulus" 251 We shall use the basic equations in terms of "stimulus" to solve the problem on creep stability of rectangular plate _(a > b) with simply supported edges and compressed in the direction of long edges . . • Geometric equations () • Relations moment - stress J h/2 ; = ;zdi, h- thickness.· () - h/ 2 • Physical equations Using the theory of pseudo-bifurcation points of N-degree, from () the "elastic analogy" can be written in following form [1], [3] () where Ei;ks K [2 . UijUks] = EPEau +hi;hks)- K + N au -N(hikh;s 3 · u2 = EP [N(n- 1) - 1] ' EPn + au ( N + 1) () i,j,k,s = 1,2 • The equilibrium equations ANi;,; = 0 AMii,ii + Ni~AW,i; = .