In[]:=
Clear["Global`*"]​​​​lineLoad=F1+I*F2;​​poissonR=ν;​​modulusE=;​​​​(*ComplexPotentialFunctions*)​​Ω=-((lineLoad/(8*Pi*(1-poissonR))))*Log[z]​​ω=(((lineLoad*(3-(4*poissonR)))/(8*Pi*(1-poissonR))))*Log[z]​​​​​​displacement=((1+poissonR)/modulusE)*ComplexExpand[(((3-4*poissonR)*Ω)-(z*Conjugate[D[Ω,z]])-(Conjugate[ω])),TargetFunctionsConjugate]*(E^(-I*θ))//FullSimplify​​u1=ComplexExpand[Re[displacement],TargetFunctionsConjugate]/.zr*(E^(I*θ))//FullSimplify​​u2=ComplexExpand[Im[displacement],TargetFunctionsConjugate]/.zr*(E^(I*θ))//FullSimplify​​​​​​
Out[]=
-
(F1+F2)Log[z]
8π(1-ν)
Out[]=
(F1+F2)(3-4ν)Log[z]
8π(1-ν)
Out[]=
-
-θ

(1+ν)2F2(-3+4ν)Log[z]+(F1-F2)1+(-3+4ν)Log[
2
z
]
8π(-1+ν)
Out[]=
-
(1+ν)Cos[θ]F1+2F2(-3+4ν)Log[
θ

r]+(F1-F2)(-3+4ν)Log[
2θ

2
r
]-F2Sin[θ]
8π(-1+ν)
Out[]=
(1+ν)F2Cos[θ]+F1Sin[θ]+(-3+4ν)2F2Log[
θ

r]+(F1-F2)Log[
2θ

2
r
]Sin[θ]
8π(-1+ν)