# principal directions

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## principal directions

[′prin·sə·pəl di′rek·shənz]
(mathematics)
For a point on a surface, the directions in which the normal curvature attains its absolute maximum and absolute minimum values. The directions of the principal axes of a strain.
References in periodicals archive ?
The current meeting is the continuation of the discussion of principal directions and strategy tasks.
The tread has a concave profile according to a plane passing through the axis of revolution, and the pneumatic tire comprises two annular ridges which extend, respectively, the two sidewalls in the outer radial direction and which are connected to two opposite ends of the tread, the two annular ridges defining, respectively, two principal directions which intersect at an acute angle so that, when the pneumatic tire comes into contact with soil, by being subjected to a vertical load, the two annular ridges move closer together locally.
A first frequency value of 90 Hz or above has to be provided and the resulted structure must withstand a 30 g load on all principal directions (X, Y, and Z).
As the water molecules in WM tissues tend to diffuse along fibers when contained in fiber bundles, the principal directions of ODF agree with the true synthetic fiber directions .
Despite this limitation, the Kozeny-Carman equation could still apply to direction-specific flows, where k = [k.sub.ii] and [[tau].sub.h] = [[tau].sub.h, ii] are the permeability and hydraulic tortuosity in the principal directions, respectively.
The polarization directions of shear waves rotate largely as the uniform applied stress varies while the principal directions of the stress remain unchanged.
The distinctiveness of the deviated data, its presence might enormously affect the solution model such as the distribution or principal directions of the data.
Reciprocity implies that [[bar.[alpha]].sub.e] and [[bar.[alpha]].sub.m] are real symmetric dyadics  and thus the xyz coordinate system of [V.sub.a] can be oriented to make [[bar.[alpha]].sub.e] or [[bar.[alpha]].sub.m] a diagonal dyadic with three principal directions. If the symmetry of [V.sub.a] is such that the three principal directions for [[bar.[alpha]].sub.e] and [[bar.[alpha]].sub.m] are the same, and [E.sub.0] (and thus [p.sub.1] and [p.sub.2]) are in one of these principal directions, then (44) reduces to
where E and v are the material properties of aluminium layers; and ET, EL are Young moduli in principal directions, GLT is shear modulus, and [v.sub.12] is Poisson's ratio of composite layers.
Lade , by using the method proposed by Pietruszczak and Mroz , related the loading directions to the principal directions of the cross-anisotropic microstructure arrangement of the particles.
For the three principal directions, the explicit solutions to the eigenvalue problem are easily computed using Maple (http://www.maplesoft.com), and are given in Table 1.

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