However, the spherical part of the tensor of permeability also depends on the orientation of the principal axes of stresses relative to the magnetic field. Under the assumption of weak magnetic dependence of the elastic properties, we deduce simplified expressions for the triaxial and plane stressed...
follows that the shear stresses are everywhere zero in a fluid at rest and inequilibrium, and from this it follows that the pressure (that is,forceper unit area) acting perpendicular to all planes in the fluid is the same irrespective of their orientation (Pascal’s law). For an isotropic...
The right-hand side of (8.13) is zero only when one of the principal curvatures of the surface is zero. This is so, for example, when the deflected shape forms part of the surface of a cylinder having any kind of cross-section. It may be mentioned that (8.13) is valid only when ...
when loadings are cyclic or unsteady, stresses can effect a material more severely. The additional stresses associated with flaws and cyclic loading may exceed the stress necessary for a material to fail. Stress intensity within the body
Using the Saint-Venant's principle, show that such a corrective solution may be generated using a simple strength of materials approximation incorporating axial and bending stresses of the form σ(c)z = Ax + By + C where A, B, and C are constants. Using principal centroidal x,y-axes, ...
follows that the shear stresses are everywhere zero in a fluid at rest and inequilibrium, and from this it follows that the pressure (that is,forceper unit area) acting perpendicular to all planes in the fluid is the same irrespective of their orientation (Pascal’s law). For an isotropic...
Looking for radar range equation? Find out information about radar range equation. An equation which expresses radar range in terms of transmitted power, minimum detectable signal, antenna gain, and the target's radar cross section... Explanation of rad
It is shown that the constant temperature mechanical behavior (i.e. the constitutive relationships) of brittle rock can be described by three equations which relate the three principal stresses and the three principal nonelastic strains resulting from void growth (i.e. microcracking) occurring within...
For a given crystal symmetry, the refractive index can be represented by an ellipsoid known as the indicatrix (Rossi, 1959). When the x, y, and z coordinate axes are chosen to be along the principal axes of the dielectric tensor, the indicatrix is the ellipsoid defined by (14)x2nx2+y...
In mechanics, the eigenfunctions of the stiffness matrix (Hessian) of some nonlinear energy—which become the Laplacian eigenfunctions for a certain energy—correspond to principal vibration modes to which the shape resonates most, under external forces and perturbations without damping. The corresponding...