A Finite Element Analysis of Laminated Anisotropic Tubes

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Abstract
To gain needed insight into the effects of thickness to diameter ratio ( t/D i), length to diameter ratio (l/Di ), and helical angle (α) on the response of laminated tubes in material characterization tests, a unique new elasticity finite element program has been implemented which can deal with the general three-dimensional nature of axisym metric composite bodies. The program, which is utilized here to analytically predict the response of unidirectional composite tube specimens to uniaxial tension/compression, differs from the usual finite element formulations in that it accounts for general anisotropy. In particular, it deals with all shear coupling terms and all six com ponents of stress. The effects of different gripping methods are also considered. Similar studies of torsion and internal pressurization tests will be reported in subsequent notes. This first phase of the study shows that while the response of axial and hoop wrapped tubes (α = 0°, 90°) is essentially indepen dent of length and thickness ratios, the effects of these ratios and helix angle can be significant for uniaxial off-axis specimens. In addition to axial stress, hoop and in-plane shear stresses are also present in the gage section, even when the grips are free to rotate. More importantly, however, the t/D i and l/Di ratios can significantly affect the mode of stress distribution. For example, the stresses are nonuniform across the tube thickness; the nonuniformity increases as the t/D i ratio is in creased, with maximum stress occurring at the inner radius. For the material considered (boron) the distributions will be effectively linear for t/Di < 0.1, while for t/Di > 0.1 they will be nonlinear. When t/D i < 0.02, the trends are nearly uniform outside the transition zones and can thus be characterized by classical shell theory formulations. The transition length ( lt) measured in from the gripped ends is ap proximated as a function of the thickness and length ratios and is given in expression (4). Interlaminar shear and radial stresses, for all practical purposes, are non-existent in the gage length (for uniaxial layups) and are of consequence only in the grip section.

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