Response and Failure of Internally Pressurized Elliptical Composite Cylinders
McMurray, Jennifer Marie
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Presented is an overview of a semi-analytical solution which was developed to study the response of internally pressurized elliptical composite cylinders with clamped boundaries. Using a geometrically linear analysis and the solution scheme, the response of a quasi-isotropic elliptical cylinder is compared with the response of a quasi-isotropic circular cylinder in order to study the effects of elliptical geometry. The distinguishing features of the response of an elliptical cylinder are the inward normal displacement of the cross section at the ends of the major diameter that occur despite the outward force of the internal pressure, the presence of circumferential displacements, and the presence of inplane shear strains. These effects lead to spatial variations, including sign reversals, of a number of displacement, strain, and curvature responses. The responses of a quasi-isotropic elliptical cylinder evaluated using a geometrically linear analysis are then compared to the responses evaluated using a geometrically nonlinear analysis. It is shown that geometric nonlinearities tend to flatten certain responses at the ends of the minor diameter, and reduce the magnitude of certain responses in the boundary region. To study the influence of material orthotropy, the responses of axially-stiff and circumferentially-stiff elliptical cylinders evaluated using geometrically nonlinear analyses are examined. It is shown that in some instances material orthotropy can be used to mitigate the influence of the elliptical geometry and make particular responses look like those of a circular cylinder. An evaluation of failure using the maximum stress and Hashin failure criteria and geometrically linear and nonlinear analyses is presented for elliptical cylinders. These failure criteria involve interlaminar shear stresses which are computed by integrating the equilibrium equations of elasticity through the thickness of the cylinder wall. The failure criteria are used to assess the mode of failure (e.g., tensile or compressive fiber or matrix modes), the location of failure, and the pressure at failure. Both criteria predict first failure to occur at the clamped boundaries because of matrix cracking. The predicted failure pressures and circumferential locations are very similar for the two criteria, and the nonlinear analyses predict slightly higher pressures at somewhat different circumferential locations. First fiber failure is also considered. For this failure the two criteria predict similar failure scenarios for the linear analyses, but they differ in their predictions for the nonlinear analyses. Specifically, using the maximum stress criterion, the circumferentially-stiff elliptical cylinder is predicted to fail due to fiber compression, but the Hashin criterion predicts failure to be due to fiber tension, and at a different circumferential location. Also, first fiber failure pressures are at least a factor of two greater than the first matrix failure pressure.
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