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On the elastoplastic stability of a plate under shear forces, taking into account its real bending form

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Using the theory of elastoplastic processes and the modified elastic solution method we investigate the stability outside elastic limit problem of a plate under shear forces, taking into account its real bending form after the loss of stability. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001, No 1 (6 - 16) ON THE ELASTOPLASTIC STABILITY OF A PLATE UNDER SHEAR FORCES, TAKING INTO ACCOUNT ITS REAL BENDING FORM DAO HUY BICH Vietnam National University, Hanoi ABSTRACT. Using the theory of elastoplastic processes and the modified elastic solution method we investigate the stability outside elastic limit problem of a plate under shear forces, taking into account its real bending form after the loss of stability. An expression for determining the critical force is obtained and numerical calculations with various ratio · of thickness have been fulfilled, from the results one can see the convergence of the modified elastic solution method . 1. Introduction From the experimental results one can see that the bending form of the plate under shear forces after the loss of stability has a form of somewhat plane sloping roofs, the nodes of which are nearly straight lines. In the investigated case of a long elastic plate under shear forces , the slope makes with the long edge an angle about 54° and the distance between the slopes is equal to 1.22 times of the plate width. In the case of elastoplastic stability of a plate subjected to axial and shear forces, . considered in [1], because of the complicatedness the author proposes some assumptions about the bending form. For reflecting the reality the real bending form must be taken into consideration of the elastoplastic stability of plates under shear forces. 2. Formulation of the problem and the solving method Suppose a long plate of width b subjected to the shear forces T along its long edges y = O and y = b (see Fig. 1). At any moment t there exists a membrane plane stress in the plate $ -" - - --!. - Fig.1 6 - ' ( s) = Et (s) : ITu ./3T A=-=-=Ee(s) , s s where Et (s) - the tangential modulus, Ee( s) - the secant modulus of the material 9b2 and with denotation i 2 = h 2 , the equation (2.10) becomes i .2 2 2 2 1( 2)2 (Et(s) 7r J3[ 2 )( 1 .