Consider the elliptical hole problem in Example 11.7. By letting a0, determine the stress field for the

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Consider the elliptical hole problem in Example 11.7. By letting a→0, determine the stress field for the case where the hole reduces to a line crack of length 2b. Demonstrate the nature of the singularity for this case.

Data from example 11.7

Consider next an infinite anisotropic plate with a stress-free elliptical hole. The plate is loaded in the x

A1 = 42 = S 2 (a2  a1) + (83  i) F (a  a2)S + 2(2  a1) + (83  ;)] ''282 (12  1) + (83  Bi) - - - with

. ----- dy = Re -Re I = - iSb (1  2)(a+iu b) iSb (11  2)(a+iub) isb (41  2)(a + iu b) {z  (a + ujb) 22 { 3

Consider now the special case of an orthotropic material with u;= i. For this case, the stress ox along theS X+ 1) q S

Investigating the value of this stress at the edge of the ellipse (y= b), we get (0, b) = s[1- - (B + B2) 1/1

Table 11.2

Table 11.2 Typical Elastic Moduli for Some Planar Orthotopic Composite Materials Material E (GPa) E (GPa) 50

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