Three wrong expressions in the paper (1) have been found. Equations (4) and (5) in the paper are written in the forms  
φIIz=iφz,ψIIz=izψz+2izφ¯z,
(1)
 
uiII=yui,xxui,y
(2)
 
σijII=yσij,xxσij,y+12σij,xdy12σij,ydxi,j=1,2.
(3)

1 Complex potentials suggested by Muskhelishvili should be an analytic function (2). However, since the argument z¯ is involved in the second term of ψIIz in Eq. (1), ψIIz cannot be an analytic function. Therefore, ψIIz in Eq. (1) is a wrong expression.

2 In the complex variable function method, the displacement components can be expressed as (2)  
2Gu+iv=κφzzφz¯ψz¯=κφz+z{φz}¯ψz¯
(4)
where G is the shear modulus of elasticity, κ=3ν/1+ν is for the plane stress problem, κ=34ν is for the plane strain problem, and ν is the Poisson’s ratio, and φz and ψz are two analytic functions.

Equation (4) reveals a rule that in a real displacement expression of plane elasticity, if the function after the elastic constant κ is φz, the term after z in Eq. (4) should be φz¯.

On the other hand, from Eq. (4) we have  
2Gux+ivx=κφzφz¯zφz¯+ψz¯
 
2Guy+ivy=i{κφzφz¯+zφz¯+ψz¯}.
(5)
Therefore, from Eqs. (2) and (5), the displacement components in Eq. (2) can be expressed as  
2GuII+ivII=2Gyux+ivxxuy+ivy=κ{izφz}+z{iφz¯z¯φz¯}iz¯ψz¯.
(6)
From the fact that  
ddz{izφz}¯=iφz¯+z¯φz¯iφz¯z¯φz¯
(7)
and the rule mentioned above, the displacements uII and vII shown in Eq. (2) are not an elasticity solution. Therefore, the displacement shown in Eq. (2) is also a wrong expression.
3 In Eq. (3) an indefinite integral is used to express the stress components. In the continuum medium of elastic body, the integral should be path-independent. Also, it is well known that if a function Fx,y 
Fx,y=xo,yox,ypx,ydx+qx,ydy
(8)
is a path independent integral, the following condition must be satisfied:  
px,yy=qx,yxorqx,yxpx,yy=0.
(9)
If Eq. (3) were true, substituting px,y=σij,y/2 and qx,y=σij,x/2 into Eq. (9) yields the following:  
2σijx2+2σijy2=0.
(10)
However, the stress components σij are not a harmonic function in general. Thus, the σijII shown by Eq. (3) is also a wrong expression.
1.
Shi
,
J. P.
,
Liu
,
X. H.
, and
Li
,
J. M.
,
2000
, “
On the Relation Between the L-integral and the Bueckner Work-Conjugate Integral
,”
ASME J. Appl. Mech.
,
67
, pp.
828
829
.
2.
Muskhelishvili, N. I., 1953, Some Basic Problems of Mathematical Theory of Elasticity, Noordhoof, Dordrecht, The Netherlands.