A Finite Element Analysis of Laminated Anisotropic Tubes

Abstract

To gain needed insight into the effects of thickness to diameter ratio ( t /D i ), length to diameter ratio (l/D i ), and helical angle (&alpha;) 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 axisymmetric 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 components 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 (&alpha; = 0&deg;, 90&deg;) is essentially independent 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/D i 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 increased, 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/D i > 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 ( l t ) measured in from the gripped ends is approximated 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.

Effect of Length on Laminated Thin Tubes Under Combined Loading

“…The additional terms account for tube gripping and length. Except for an isolated region near the grips, solutions give nearly identical results; and based on the findings in [1] both should be accurate for mid-plane displacements and resultant stress predictions in the range tIDi < 0.05 and LlD~ > 3. As an example of the solution, Figure 2 shows the radial displacement t7,. for a thin 1 in.…”

“…diameter boron tube, « = 30°, under pure axial extension. Also shown are the results obtained using the finite-element method of [1]. CONCLUSION A solution in the context of shell theory has been developed for balanced laminates which reflect the effect of tube length.…”

“…For strength determinations, however, curvature 1IDi becomes important. This aspect is delineated in [ 1 ], where it is found that a degradation of accuracy occurs with increasing curvature (i.e., decreasing diameter).…”

“…A. VICARIO AND R. R. RIZZO, Hercules Incorporated, Allegany Ballistics Laboratory, Cumberland, Maryland 21502 (Received January 24, 1970) The use of thin-wall laminated cylindrical tubes is currently of considerable interest for the material property characterization of hard composites. In view of this interest, a numerical finite-element analysis has been reported in Reference [ 1 ] which characterizes tube responses to axial tension/compression, torsion and internal pressurization as a function of the tube geometry, material, ply orientation and end constraints. In brief, it was found that for infinitely long tubes an accurate prediction of tube behavior can be obtained from the closed form solution of Sherrer [2].…”

“…In view of this interest, a numerical finite-element analysis has been reported in Reference [ 1 ] which characterizes tube responses to axial tension/compression, torsion and internal pressurization as a function of the tube geometry, material, ply orientation and end constraints. In brief, it was found that for infinitely long tubes an accurate prediction of tube behavior can be obtained from the closed form solution of Sherrer [2].…”