Sxrl [B] [C] {xI [B] {x-[ [C]{ y
 A{z}=[A]{Z}= [A
 { y) [I] 0 _{y y {x!

 (A19)

 where


 {Z}= {x}= X, = Z,, {y}= Y, Z, (A20)
 X, Z3 Y3 Z6

 {A{X}) [B]{X- [C]{Y}} (A21)
 =e- ^ I (A 21)
 A{Y}j {x}

 A{x}=-[B]{X}-[C]{Y} and {X)= A{Y}

 These two equations can be combined into one equation by substituting for X,

hence eliminating X, and rearranging terms.

 [22[] + A[B] + [C]](Y}= 0 (A22)

 Comparing Eq. A22 yield the necessary eigenvalues and eigenvectors


 A=P, and {Y}= Y, = Z, ={v} (A23)
 Y3 Z6

 Comparing Eq. A23 and verifies that equation can be used to solve for PL as

eigenvalues instead of roots to the characteristic equation derived from the determinate of

the coefficient matrix in equation. Both eigenvalues, PL, and eigenvectors from equation

will be used in the next section to calculate the singular exponent. The general solution of

the displacement and stress is formulated using the Stroh's method Ting and Hoang [1].


(A24)


u, = r1-k La Re (,-k)+ii L -k)}/(l k)