Modelling of non-steady creep of bending reinforced plates made of nonlinear hereditary materials

Abstract

On the basis of the equations of nonlinear hereditary Rabotnov’s theory of creep and the idea of the method of time steps, the problem on the rheonomic behavior of quasistatically bending plates cross- reinforced in their plane is formulated as the geometrically linear problem. The equations and relations are obtained to determine, at discrete points in time with different degree of accuracy, the stress-strain state of composite plates with account of their weak resistance to transversal shifts. The relations of the classical theory and the traditional non-classical Reissner and Reddy theories follow from the resulting equations as special cases. A model problem is considered for asymmetrically reinforced and loaded annular plates which are rigidly clamped on one edge and uniformly loaded on another edge. For this case a simplified version of the refined theory is developed, which has roughly the same implementation complexity as the theory of Reissner and Reddy. The specific calculations are carried out for the flexural deformation of the considered annular plates with spiral and spiral-circumferential reinforcements at short-term and long-term loading. It is demonstrated that, for composite plates (including metal matrix), with the relative thickness of the order of 1/10, neither the classical theory nor the theory of the Reissner and Reddy type do not guarantee reliable results for the determination of the deflection even under rough 10% accuracy. The accuracy of the calculations for these theories decreases with increasing time of long-term loading of reinforced structure. Using the equations of the refined theory, it has been found that in the process of bending flat reinforced plates, in some cases (e.g. for low-strong binders and high-modulus fibers), the strongly-pronounced boundary effects occur in a neighborhood of the supported edges, which characterize a sudden shift of these structures in transverse direction. It is shown that even at very low levels of lateral load, when the deflection is amount to only a few percent of the thickness of the reinforced plate, the strain in the binder can reach 5 % or more under long-time loading.