On the invariant representation of spin tensors with applications

The invariant representation of the spin tensor defined as the rotation rate of a principal triad for a symmetric and non-degenerate tensor is derived on the basis of the general solution of a linear tensorial equation. The result can be naturally specified to study the. spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics. A remarkable formula which relates the generalized stress conjugate to the generalized strain in Hill's sense. to Cauchy stress, is obtained in invariant form through the work conjugate principle. Particularly, a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes of strain arc not fixed during deformation.

Objective speckle method using stick-on foil and its applications

Objective speckle from a stick-on foil is a new approach to applying the objective white light speckle method to in-plane displacement measurements. By a relatively easy technique a thin aluminum foil is mounted onto the specimen surface and a random grating is scratched onto it, yielding high reflectance and fine optical details. After double exposure by a direct recording system without using a lens, the resulting holographic film possesses a broad spatial spectrum and displacement information. Full-field contour maps of equal displacement can be obtained that are of good contrast and high sensitivity and that have a large adjustable measurement range. The method can be applied to practical engineering problems for both plane and developable curved surfaces.

Generalized rayleigh principle and its applications

In this paper, we mainly deal with cigenvalue problems of non-self-adjoint operator. To begin with, the generalized Rayleigh variational principle, the idea of which was due to Morse and Feshbach, is examined in detail and proved more strictly in mathematics. Then, other three equivalent formulations of it are presented. While applying them to approximate calculation we find the condition under which the above variational method can be identified as the same with Galerkin's one. After that we illustrate the generalized variational principle by considering the hydrodynamic stability of plane Poiseuille flow and Bénard convection. Finally, the Rayleigh quotient method is extended to the cases of non-self-adjoint matrix in order to determine its strong eigenvalne in linear algebra.