Two-parameter asymptotic analysis of the dynamical equations of the theory of elasticity for the bending of a plate☆

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Abstract

The three-dimensional dynamical equations of the theory of elasticity for the bending of a plate are subjected to asymptotic analysis. Two dimensionless parameters (the exponents of variability and dynamism) characterizing the stress-strain state (SSS) of the plate are varied independently. The asymptotic behaviour of the SSS is established for different parameter values. Cases are found in which the equations of classical plate theory do not furnish a first asymptotic approximation of the equations of the theory of elasticity.

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    Asymptotic analysis and improved versions of the Timoshenko-Reissner plate and shell theories

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Cited by (1)

☆

Prikl. Mat. Mekh. Vol. 56, No. 5, pp. 750–755, 1992.

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