A pair of complex conjugate fourth-order differential equations that govern the deformation of orthotropic circular cylindrical shells is presented. As shown in the paper, this pair of equations is as accurate as equations can be within the scope of the Kirchhoff assumptions. Also presented for the first time are several pairs of accurate and simple fourth-order equations which can be systematically and explicitly deduced from the previously mentioned pair of equations. Because of their accuracy and simplicity, these simple equations are of practical importance. The advantage in applying those fourth-order equations presented herein is that their solutions can be easily found in simple closed forms. This considerably simplifies calculations for solving problems of orthotropic and composite cylindrical shells as well as isotropic shells as a special case. Unlike other equations known in the literature, their general solutions remain unknown because of the algebraic complexities involved. The present method of deducing simple fourth-order equations improves upon the one used for isotropic shells in the first author’s previous paper entitled “Accurate Fourth-Order Equations for Circular Cylindrical Shells,” Journal of the Engineering Mechanics Division, ASCE, 1972.

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