Advanced high order theories and elasticity solutions for curved sandwich composite panels
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A new one-dimensional Extended High order Sandwich Panel Theory (EHSAPT) for curved panels is presented. The theory accounts for the sandwich core compressibility in the radial direction as well as the core circumferential rigidity. Two distinct core displacement fields are proposed and investigated. One is a logarithmic (it includes terms that are linear, inverse, and logarithmic functions of the radial coordinate). The other is a polynomial (it consists of second and third order polynomials of the radial coordinate) and it is an extension of the corresponding field for the flat panel. In both formulations the two thin curved face sheets are assumed to be perfectly bonded to the core and follow the classical Euler-Bernoulli beam assumptions. The new theory is formulated by Principle of Minimum Total Potential Energy for static and Hamilton's principle for free vibration analysis. Then, the linear elasticity displacement formulation and solutions for a generally asymmetric simply support sandwich curved beam/panel consisting of orthotropic core and face sheets are presented. Closed-form analytical solutions are derived for the curved sandwich subjected to a top face distributed static transverse loading; and the method of Frobenius series is applied in free vibration analysis. Next, due to the curvature, the first order shear deformation (FOSD) theory for curved sandwich panels is not a direct extension of the corresponding one for flat panels and thus, it is formulated accordingly, and its unique features, such as the reference curve, are discussed. Three versions of the FOSD theory are formulated: the one based on direct variational formulation based on the assumed through-thickness displacement field (termed "basic''), one based on the definition of an equivalent shear modulus for the section (termed "Geq") and one based on derivation of a shear correction factor, which is considered in conjunction with the equivalent shear modulus. In addition, the classical theory for curved sandwich panels which does not include transverse shear is also presented. The results from following: the new proposed EHSAPT, the existing high order sandwich panel theory HSAPT (from literature), three variants FOSD theory, and Classical theory are compared with Elasticity which serves as a benchmark in assessing the accuracy of the various sandwich panel theories. The case examined are transverse static loads and free vibration of simply supported curved sandwich panels, for which a closed form elasticity solution is formulated. It is shown that the new EHSAPT is the most accurate among other presented theories with the logarithmic formulation is more accurate than the polynomial.