Jq. Tarn, AN ASYMPTOTIC THEORY FOR NONLINEAR ANALYSTS OF MULTILAYERED ANISOTROPIC PLATES, Journal of the mechanics and physics of solids, 45(7), 1997, pp. 1105-1120
An asymptotic theory for nonlinear analysis of multilayered anisotropi
c plates is developed on the basis of three-dimensional nonlinear elas
ticity without making a priori assumptions or omitting any nonlinear t
erms in the formulation. The laminated plate is regarded as an anisotr
opic heterogeneous plate with material properties varying in the thick
ness direction. Reformulation and nondimensionalization of the 3D equa
tions of nonlinear elasticity reveal that the analysis can be carried
out by means of asymptotic expansion and successive integration. It is
shown that the von Karman nonlinear theory of laminated plates arises
naturally as the first-order approximation to the 3D theory. Higher-o
rder corrections can be determined systematically. In the formulation
the boundary conditions on the top and bottom surfaces of the plate ar
e satisfied and appropriate edge conditions associated with each level
are derived. The theory accounts for the nonlinear effects in an adap
tive and hierarchic way. There is no need to treat the system layer by
layer or to consider the interfacial continuity conditions in particu
lar. (C) 1997 Elsevier Science Ltd.