DISCUSSION ON THE SIF FOR POINTS ON BORDER OF ELLIPTICAL FLAT CRACK INSIDE INFINITE SOLID UNDER UNIFORM TENSION

摘要/Abstract

摘要： Using the results of crack surface displacement field in Green-Sneddon’s solution[1] and coordinate transformation, this paper has derived an expression K₁(x₁,z₁,a) for SIF at any point and at any orientation on the border of elliptical flat crack inside infinite solid under uniform tension. As a complement of Irwin’s work[3], it is shown that for any pointed point on the elliptical border the SIF defined on normal plane takes the maximum value. And it should be pointed out that in some works some idea concerning Irvin’s contents is open to question. An expression K₁ in terms of polar angle which is more intuitional than centrifugal angle is proposed for SIF at any point on the elliptical border.

关键词: option, Black-Scholes formula, differential equation

Abstract: Using the results of crack surface displacement field in Green-Sneddon’s solution[1] and coordinate transformation, this paper has derived an expression K₁(x₁,z₁,a) for SIF at any point and at any orientation on the border of elliptical flat crack inside infinite solid under uniform tension. As a complement of Irwin’s work[3], it is shown that for any pointed point on the elliptical border the SIF defined on normal plane takes the maximum value. And it should be pointed out that in some works some idea concerning Irvin’s contents is open to question. An expression K₁ in terms of polar angle which is more intuitional than centrifugal angle is proposed for SIF at any point on the elliptical border.

Key words: option, Black-Scholes formula, differential equation

蔡增伸. DISCUSSION ON THE SIF FOR POINTS ON BORDER OF ELLIPTICAL FLAT CRACK INSIDE INFINITE SOLID UNDER UNIFORM TENSION[J]. Applied Mathematics and Mechanics (English Edition), 1982, 3(4): 521-526.

Cai Zeng-shen. DISCUSSION ON THE SIF FOR POINTS ON BORDER OF ELLIPTICAL FLAT CRACK INSIDE INFINITE SOLID UNDER UNIFORM TENSION[J]. Applied Mathematics and Mechanics (English Edition), 1982, 3(4): 521-526.

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