Abstract:
An initial-boundary value problem is formulated to describe the dynamic behavior of flexible longitudinally reinforced wall-beams of the lesser curvature. Mechanical behavior of materials of composition of the beams is described by the equations of the theory of plasticity with isotropic hardening. The geometric nonlinearity of the problem is considered in the Karman approximation. The obtained equations and correlations allow with different degree of accuracy to determine the stress-strain state of the considered beams taking into account of their weakened resistance to the transverse shears. From the received relationships in the first approximation the equations, corresponding to the second variant of Timoshenko theory, are obtained. For the numerical integration of the problems the method of steps in time with the involvement of the central differences to approximate derivatives with respect to time, is used. The longitudinally reinforced straight and slightly curved beams-walls of relatively low height are considered. The dynamic response is investigated for the considered constructions depending on the action surface (concave or convex) of external pressure caused by the arrival of the air blast wave. It is found that at the time intervals exceeding a few tenths of fractions of a second, elastic-plastic behavior of flexible reinforced straight and curved wall-beams, determined according to the second variant of the Timoshenko theory, is significantly different from the inelastic dynamic response calculated according to the refined theory.
Keywords:flexible beams, reinforcement, geometric nonlinearity,
dynamic deformation, theory of plastic flow, isotropic hardening, second
variant of Timoshenko theory, numerical integration, “cross” scheme.
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