Application of the variational-asymptotical method to laminated composite plates
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Hodges, Dewey H.↗
Engineering topics
Lee, Bok W.
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A variable-order laminated plate theory based on the variational-asymptotical method
The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.
Lee, Bok W.↗
Application of the variational-asymptotical method to composite plates
A method is developed for the 3D analysis of laminated plate deformation which is an extension of a variational-asymptotical method by Atilgan and Hodges (1991). Both methods are based on the treatment of plate deformation by splitting the 3D analysis into linear through-the-thickness analysis and 2D plate analysis. Whereas the first technique tackles transverse shear deformation in the second asymptotical approximation, the present method simplifies its treatment and restricts it to the first approximation. Both analytical techniques are applied to the linear cylindrical bending problem, and the strain and stress distributions are derived and compared with those of the exact solution. The present theory provides more accurate results than those of the classical laminated-plate theory for the transverse displacement of 2-, 3-, and 4-layer cross-ply laminated plates. The method can give reliable estimates of the in-plane strain and displacement distributions.
Hodges, Dewey H.↗