[alpha] is crack length (urn); [beta] is reliability index; G(Xj) is the limit state function; [K.sub.I] is stress intensity factor in mode I (MPa.[square root of (term)]m); [K.sub.IC] is critical stress intensity factor (MPa.[square root of (term)]m); p is operating pressure (MPa); [P.sub.f] is probability of failure; P is probability operator; r is pipe radius (mm); SDR is standard dimension ratio; t is wall thickness (mm); [X.sub.j] is random variables; Y is

geometrical factor; [[sigma].sub.max] is stress max (MPa); [[sigma].sub.e] is yield stress (MPa); [PHI](-[beta]) is cumulative Gaussian probability function.

Where [P.sub.c] is the fracture load, a is crack length, w is the specimen width, t is the specimen thickness, and f(a/w) is a

geometrical factor. In turn [K.sub.IC] and [K.sub.IIC] are obtained using

geometrical factors or nondimensional stress intensity factors [f.sub.I](a/w) and [f.sub.II](a/w), respectively, which are obtained through finite element analysis of test specimen.

Geometrical factor of electrodes is calculated according to following equation

where [eta] is the

geometrical factor depending on the ratio of p = ([r.sub.k] - w)/[r.sub.k].

[[chi].sub.m] is expressed in terms of the physical factor P and

geometrical factor F as:

Geometrical factor, [F.sub.g] = [Z.sub.c]/ [F.sub.g] [Z.sub.o], k = 0.7513 8.

In other words, M* is a

geometrical factor and it depends on the way the bending moment is applied.

J-Parameter Based Upon the Ubiquitous

Geometrical Factor [eta]

Using the membrane permeation model, the effective diffusion coefficient is measured by measuring polymer intrinsic diffusion coefficient and solubility of the gas component in the polymer matrix for all the gases involved (14, 15): it is also necessary to assume a

geometrical factor that accounts for the influence of foam morphology on the effective diffusion coefficient.

Because the former angle is larger than the latter one, geometrical optics suggests that the total power detected depends only on the blackbody temperature and a

geometrical factor related to the pinhole aperture, detector optics, and relative separation, because the detector pupil is overfilled.

Li, the expressions of stiffness coefficient, thermal stress, and thermal moment for hybrid laminates were derived based on the

geometrical factors of laminates, and the necessary and sufficient conditions for the hybrid extension-shear coupled laminates with immunity to hygrothermal shear distortion (HTSD) were further derived.

We are also working on reporting other aneurysm

geometrical factors that contribute to failure of flow-diversion; however this work is still in its early stages.