On linear equations of anisotropic elastic plates

Yi-Yuan Yu
1965 Quarterly of Applied Mathematics  
Introduction. In a previous paper [1] a generalized Hamilton principle and the associated variational equation of motion are presented for finite elastic deformations. The principle is a generalization of the ordinary Hamilton principle in which only variations of the displacements are admitted. It is also a generalization of the variational principle in elastostatics due to Hu [2]** and Washizu [3], and is similar to the latter in that in both principles variations of the displacements,
more » ... splacements, strains, and stresses are taken independently and simultaneously. Various complete systems of equations of nonlinear elastodynamics have been shown to be obtainable as the Euler equations of the generalized Hamilton principle. In this note the generalized Hamilton principle and the associated variational equation of motion for linear and anisotropic elastic plates are deduced from their counterpart in general elasticity theory given in the previous paper [1], through expansion of the displacement and strain in infinite power series in the manner of Cauchy and Mindlin [4, 5] and by carrying out the integration in the thickness direction of the plate. The Euler equations of the variational principle then yield the complete system of plate equations of all orders as were obtained by Mindlin by a different procedure. Some zeroorder and first-order equations for an isotropic plate have been derived before [1] from the generalized variational equation of motion.
doi:10.1090/qam/187498 fatcat:wz3552gihfhs5atxjun6ozffq4