Boundary Point Least Squares Analysis of the Free Edge Effects in Some Unidirectional Fiber Composites

Abstract

The effect of a free edge on the stress distribution in several uni directional composite plates is presented. Plates with one, two, and three rows of equally spaced fibers are considered. The fibers and matrix are elastic and isotropic. Two types of loading conditions are investigated. The first is a uniform extension transverse to the fiber direction. The second is a linearly varying "bending" displacement transverse to the fiber direction. Stress and displacement solutions are obtained by the boundary point least squares method. For both loading conditions considered, the results show that the effect of the free edge extends only to the outer fiber nearest the free edge and the stress distribution in and around the remaining "inside" fibers is essentially equivalent to stresses for a fiber embedded in a doubly periodic array. For the case of uniform extension, effective transverse moduli are computed for the one, two, and three fiber plates and compared with the effective transverse modulus for an infinite plate.

48414 Measurements of elastic constants of thin AlO and SiC/Al composite using coupled ultrasonic plate modes

“…This question has been partially addressed previously [9], where, however, a numerical study was performed for only one elastic constant and no experimental data were shown. A comparison is shown in Table 1, where the models of Christensen [6] and Nielsen [7] are used.…”

An Experimental and Numerical Investigation of the Free Edge Problem in Composite Laminates

“…The six equations of compatibility reduce to only three nontrivial equations since the variables are independent of the x coordinate. Using the first two of Equations (3), and the stress-strain relations for an orthotropic material, we may write (4) Rearranging terms (see Appendix A) in the above equation gives (5) The stress states can be expressed in terms of the stress functions via Equations (2), which leads to the following pair of coupled partial differential equations: (6) We can convert the above equations to a pair of ordinary differential equations, following the method of Mushkelishvili [51], by defining where µ is a complex variable. Using this definition it can be shown that Equations (6) reduce to (7) It can be shown further that the above equation implies the following forms for the stress functions:…”

Theoretical Post-Yielding Behavior of Composite Laminates Part I—Inelastic Micromechanics

“…Another question regarding the applicability of elastic-plastic analysis to boron fiber reinforced plastics has been raised in [ 11 ] . This paper, has shown that a slight variation (<10%) occurs in some of the composite elastic properties between the surface and the center plies of a laminate as a result of the presence (or absence) of constraints on the deformations that take place in the thickness direction.…”