Discussion: “Zeroth-Order Shear Deformation Theory for Laminated Composite Plates” (Ray, M. C., 2003 ASME J. Appl. Mech., 70, pp. 374–380)

Abstract

It is the contention of the authors that the “zeroth-order” shear deformation theory presented by Ray 1 is mathematically equivalent to Reddy’s third order theory 2. The notation of Ref. 1 is used herein. Ray’s approximations for the in-plane displacements u=u0−zw,x+3z2h−2z3h3 Qxλx, v=v0−zw,y+3z2h−2z3h3 QyλyDisplay Formulaare identical to those of the Reddy’s theory, 2, with Display Formulaψx+w,x=3Qx2hλx, ψy+w,y=3Qy2hλy.Hence the equations of motion and boundary conditions of Ray’s theory are mathematically equivalent to those of the dynamic version of Reddy’s theory. This is established explicitly by comparing the governing equations of the two theories.