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Three dimensional rendering of a typical buckling mode with 2 axial half-waves and 4 full circumferential waves

This slide supplied by Michael Nemeth, NASA Langley Research Center, Hampton, Virginia

Figure 4a from the report,
Michael P. Nemeth and Martin M. Mikulas, "Simple formulas and results for buckling resistance and stiffness design of compression-loaded laminated composite cylinders", NASA/TP-2009-215778, August 2009.

ABSTRACT: Simple formulas for the buckling stress of homogeneous, specially orthotropic, laminated-composite cylinders are presented that are the counterpart of the classical buckling formula for an isotropic cylinder. The formulas are obtained by using nondimensional parameters and equations that facilitate general validation, and are validated against the exact solution for a wide range of cylinder geometries and laminate constructions. The buckling stress is found to be a product of a nondimensional coefficient, that involves only material properties of the wall, with the thickness-to-radius ratio of the cylinder and the effective modulus of the corresponding quasi-isotropic laminate. Unlike the corresponding isotropic-cylinder solution, that is represented by a single equation, two equations that depend on the laminate orthotropy are needed to obtain the orthotropic-cylinder solution; one for axisymmetric and one for asymmetric buckling modes. Results are presented that establish the ranges of the nondimensional parameters and coefficients used. General results, given in terms of the nondimensional parameters, are presented that encompass a wide range of geometries and laminate constructions. These general results also illustrate a wide spectrum of behavioral trends. Design-oriented results are also presented that provide a simple, clear indication of laminate composition on critical stress, critical strain, and axial stiffness. The particular graphical form of these results that is used in the present study enables rapid trade studies for different design requirements. One conclusion found in the present study is that no buckling stress can be achieved for homogeneous specially orthotropic cylinders that is higher than the corresponding quasi-isotropic layup. Another conclusion is that the higher values of buckling stress are associated with higher values of axial strain. An example is provided to demonstrate the application of these results to thin-walled column designs.

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