No abstract

Using the photoelastic experimental hybrid method, we can obtain stress intensity factors and separate the stress components near the crack tip of any material under various loading conditions from only isochromatics. However, monochromatic light has, until now been used in the photoelastic experimental hybrid method to produce black and white isochromatics. The existing photoelastic experimental hybrid method using black and white isochromatics requires high order fringes to obtain sufficient experimental data for photoelastic hybrid techniques. If a photoelastic experimental hybrid method for colour isochromatics is developed, isochromatics with a maximum fringe order of 2 will be adequate for gathering the necessary experimental data for stress analyses using photoelastic hybrid techniques. Therefore, in this work, photoelastic experimental hybrid method for colour isochromatics of a crack problem was developed, and its superiority demonstrated by comparing its results with the results from black and white isochromatics. The use of few fringe orders in photoelastic experimental hybrid method for colour isochromatics is an important feature of this method. Because of this feature, this method, specifically the reflection type photoelastic method where low fringe orders are produced compared to the transmission type photoelastic method, can be widely used in stress analysis of real components.

Isochromatics obtained from photoelastic experiment shows the stress distributions of the full field of a structure under load.

In this paper, photoelastic experimental hybrid method using external traction free boundary condition and using the relative equation of two stress functions in contact problems are developed. Their validities are confirmed through experiments and discussions Hertz's contact theory and two photoelastic experimental hybrid methods explained above are applied to the stress analysis of O-ring under 10% or 20% squeeze rate. Among them, the photoelastic experimental hybrid method using the relative equation of two stress functions in contact problems is most effective. When squeeze rates of O-ring are 20%, Maximum of absolute x is greater than maximum of absolute y by little. But they are almost equal to each other. Maximums of absolute xy are 1/5 of absolute x when squeeze rate of O-ring 20%.

In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita.