Journal of Mathematical Sciences

, Volume 240, Issue 1, pp 48–69 | Cite as

Construction of a Refined Model of the Dynamic Behavior of Flexible Reinforced Plates of Nonlinear Elastic Materials Based on the Explicit Numerical “Cross” Scheme

  • А. P. Yankovskii

In the von Kármán approximation, we formulate the initial-boundary-value problem of dynamic deformation of flexible reinforced plates with nonlinear elastic behavior of the materials of the components of composition. We deduce the equations for the determination of the stress-strain states of these plates with different degrees of accuracy with regard for their weakened transverse-shear resistance. As a special case of these equations, we get the relations of the nonclassical Reddy theory. For the numerical integration of the posed problem, we use the method of time steps with application of the explicit numerical “cross” scheme. We investigate the dynamic response of relatively thick and thin annular composite plates containing a rigid internal washer under the action of loads caused by an air-blast wave. The plates are rigidly fixed along the outer contour and rationally reinforced in the radial and radial-circumferential directions. It is shown that, in the case of application of the “cross” scheme, the numerical procedures based on the equations of refined theories have a higher practical stability than within the framework of the Reddy theory. It is also discovered that, for times of about one second and longer, the computed dynamic behavior of the reinforced plates determined according to the Reddy theory strongly differs from the behavior determined according to the refined theories.


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Authors and Affiliations

  • А. P. Yankovskii
    • 1
  1. 1.Khristianovich Institute of Theoretical and Applied MechanicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia

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