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Nondimensional Parameters and Equations for Buckling of Symmetrically Laminated Thin Elastic Shallow Shells

Buckling behavior of laminated composite plates and shells has received
renewed interest in recent years due to the search for ways to exploit
anisotropy in the design of aerospace vehicles. The present study focuses
on buckling analysis of symmetrically laminated doubly-curved shallow
shells. These shells are candidates for aircraft applications such as wing
cover panels, empennage and fuselage skins, engine cowlings, and wing-to-
body fairings. In addition, these shells have potential spacecraft
applications such as liquid fuel tankage, pressure bulkheads, missle nose
cones, and payload modules. Understanding the fundamental parameters that
affect the performance of these shell structures, as well as the importance
of anisotropy, is a key ingredient of their design, and ultimately their
use. Moreover, these parameters can provide valuable information useful in
developing scaling laws for structural testing of plates and shells.

Symmetrically laminated shells exhibit anisotropy in the form of
material—induced coupling between pure bending and twisting deformations
that is commonly exhibited by symmetrically laminated plates undergoing
bending deformations. In addition, they exhibit anisotropy in the form of
coupling between pure biaxial stretching and membrane shearing. The
anisotropy is manifested in shell buckling theory by the presence of odd-
combination mixed partial derivatives in the partial differential equations
governing buckling and the natural or force boundary conditions. The
presence of the these derivative terms prevent simple closed form solutions
from being obtained. Studies that assess the importance of anisotropy on
buckling behavior of symmetrically laminated plates are presented in
references 1 and 2. In reference 1, nondimensionalization of the partial
differential equation governing plate buckling is presented and
nondimensional parameters are identified that provide physical insight into
plate buckling behavior. The results presented in reference 1 suggest the
potential for using nondimensional parameters to characterize plate buckling
behavior, assess the importance of anisotropy, and aid in their preliminary
design. The results presented in the present paper build upon the results
presented in reference 1.