Effects of Transverse Normal and Shear Strains in Orthotropic Shells

Abstract

Introduction P and shell structures in missile, space, and nuclear applications are often subjected to severe operational conditions. Classical methods of analysis based on the Kirchhoff-Love (K-L) hypothesis (implying neglect of transverse shear deformation and transverse normal stress) may not be applicable in such cases. This is especially true for certain composite and refractory materials which show a high degree of anisotropy in physical and mechanical properties. Typical of such materials is pyrolytic graphite (PG), perhaps the best known of the many pyrolytic refractory materials. Noteworthy among its unusual properties are the following: 1 ) PG is transversely isotropic. 2) The ratio of in-plane Young's modulus to transverse shear modulus (E/G\3) for PG varies between 20-50, as compared to E/G of 2.6 for an isotropic material with v = 0.3. 3) The ratio of transverse to in-plane thermal expansion coefficients (a33/an) varies approximately between 10 and 30. 4) The in-plane Poisson's ratio for PG is negative (v = 0.21) while the transverse ratio (v13 = 0.90-1.0) is quite high. The purpose of the present Note is to illustrate the significance of transverse shear, normal stress effects, and edge conditions on the stress and displacement computations for thin shells subjected to thermal loading and also to point out the hazards of employing classical shell theories for analysis of structures of pyrolytic graphite-type materials.