Proper conditioning of classical and applied plate theories | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 3 > №1 / 1997 / Pages: 92-99

Proper conditioning of classical and applied plate theories



A classical problem of applied elasticity theory: properly conditioned and complete construction of two-dimensional plate-theory equations from the equations of three-dimensional elasticity theory is analyzed. A step-by-step asymptotic derivation of the solving equations of the theory of transversely isotropic plates is given in the displacements with analysis of boundary conditions for both the faces and end surfaces of the plate. The resulting equations indicate that even the classical variant of plate theory requires significant corrections involving asymptotically exact consideration of the variability of the loads acting on the plate. Distinctive aspects of asymptotic derivation of applied plate-theory equations that take account of shearing deformation in the mean are established.