CONSTRUCTING EXACT DYNAMIC ELASTICITY SOLUTIONS FOR AXISYMMETRICALLY DEFORMED PLATES FROM CLASSICAL PLATE-THEORY SOLUTIONS

This paper addresses the question of how to assess the errors made whe n the exact three-dimensional linear elasticity solution for the axisy mmetric dynamic deformation of an elastic plate is approximated by a s olution inferred from the classical plate theory of Kirchhoff. Followi ng the strategy used by Ladeveze and Simmonds for beams, the exact sol ution of a ''nearby'' three-dimensionnl problem, which differs from th e original problem by the addition of incremental, computable body for ces, face shears, and initial conditions-error increments, for short-i s expressed in terms of the solution of a wave equation in which dista nce normal to the plate's midplane plays the role of a time-like varia ble while the physical ti,ne itself enters only as a parameter. The er ror increments which, ultimately, can be computed in terms of the solu tion delivered by plate theory, can be regarded as an ''engineering no rm'' because with them an engineer can decide if such a shift in the e xternal dam lies within acceptable bounds.