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In a current article, Whitney [1] has presented exact solutions for certain problems of the bending of unsymmetrically laminated plates. This note considers an approximate method of solution for such plates which, although approximate, yields solutions that compare favorably with those presented by Whitney. Furthermore, since the approximate method reduces the problem to an equivalent anisotropic bending problem, the techniques that have been developed for the analysis of orthotropic and anisotropic plates can be directly utilized. It should be noted that the possibility of using the approximate analysis discussed herein was first suggested in [2] on the basis of experimental evidence. The present note presents an explanation of why this approximation does not introduce large errors, and presents numerical comparisons with Whitney's exact solutions. BASIS OF THE APPROXIMATE ANALYSISThe total potential energy of a general laminated plate can be written in terms of the geometric midplane strains ( e ) and plate curvatures ( k ) as follows:where the elements of the matrices are defined such that the stress resultants [N] and moments [M] are given as and a superscript T denotes a transpose. The potential energy expression (1) exhibits coupling between midplane strains and plate curvatures through the coupling matrix [B]. If the constitutive Equation (2) is solved to give [e] in terms of [N] and [k], and then this expression is substituted into (1), an expression for the potential energy in terms of the stress resultants and plate curvatures can be obtained:

An energy formulation and solutions are presented for the analysis of plane anisotropic rectangular plates with various boundary condi tions. The formulation includes linear theory stability analysis, the calculation of natural frequencies and mode shapes, and analysis of displacement due to lateral loads. In-plane loadings are included in all of these formulations. The Ritz technique is used to find the minimum of energy expressions using a series expansion of beam mode shape functions. Several numerical and experimental results are presented and compared.

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