Journal of Theoretical
and Applied Mechanics

39, 4, pp. 959-968, Warsaw 2001

Micropolar plates subject to a normal polyharmonic loading

Grzegorz Jemielita
Following the previously published considerations the present paper aims at determination of a displacement vector and infinitesimal rotation vector describing the bending of the Grioli-Toupin plate subject to a normal polyharmonic loading. The presented biharmonic representation reduces the problem of equilibrium of such a plate to a non-homogeneous biharmonic equation involving a function of plate deflection. A semi-inverse method in an explicit form has been obtained together with relationships for force and moment stresses. Formulas for determination of the functions $g_i$ and $f_i$ of the variable $\xi$ and coefficients $A_i$ in a recurrent form have been given as well.
Keywords: Grioli-Toupin material; micropolar plates; polyharmonic loading