Elasticity Solutions for Sandwich Orthotropic Cylindrical Shells Under External/Internal Pressure or Axial Force

Abstract

The elasticity solution is constructed for a cylindrical sandwich shell under external and/or internal pressure and for the same shell under axial load. The solution is an extension of the one for a homogeneous, monolithic shell and is provided in closed form. All three phases, that is, the two face sheets and the core, are assumed to be orthotropic. Moreover, there are no restrictions as far as the individual thicknesses of the face sheets and the sandwich construction may be asymmetric. These solutions can be used as benchmarks for assessing the performance of various sandwich shell theories. Illustrative results are provided in comparison to the sandwich shell theory. HE need for lightweight yet stiff and durable aerospace structures has made the sandwich composite cone guration a leading-edge technology with promise for innovative high-perfor- mance structural designs. Sandwich construction is indeed increas- ingly employed in sections of rotorcraft and e xed-wing aircraft fuselages. A typical sandwich structure is composed of two thin composite laminated faces and a thick soft core made of foam or low-strength honeycomb. The majority of the literature in sandwich composites is on the plate cone guration. 1;2 Among the smaller number of studies on the sandwich shell geometry, we mention the papers by Reissner, 3 BienekandFreudenthal, 4 BakerandHerrmann, 5 Kollar, 6 Greenberg et al., 7 Birman and Simonyan, 8 and Frostig. 9 Sandwich shell theo- ries are extensions of the well-known shell theories for monolithic structuressuch as Reissner' s 3 orLove's 10 orSanders' s 11;12 shellthe- ory, with a set of additional assumptions imposed, usually that the corecarries only shearstressesand thatthe facesheetscarry thenor- mal stresses. Therefore, the extensional and bending stiffnesses of the shell are calculated exclusively from the face-sheet stiffnesses, whereas the transverse shear stress resultants are based exclusively on the shear stiffnesses of the core. Elasticity solutions are signie cant because they provide a bench- mark for assessing the performance of the various shell theories. To thisextent,thegeometry of acircular cylindricalshellisparticularly attractive for constructing elasticity solutions due to the axisymme- try that simplie es the analysis. Elasticity solutions for monolithic orthotropic cylindrical shells have been provided by Lekhnitskii. 13 However,elasticitysolutionsforsandwichcylindricalshellcone gu- rations are essentially nonexistant. Like the sandwich shell theories, elasticity solutions for sandwich shells can be obtained by properly extending the solutions for monolithic structures. (This implies, among others, enforcing the proper conditions at the interface of the constituent phases, that is, face sheets and core. )