This is a notebook containing the M.L.Williams analysis of stress concentration in the vicinity of a wedge.

<< Graphics`MultipleListPlot`
<< Calculus`VectorAnalysis`
Set Coordinates[
        Cylindrical[r, θ, z]]
F[{r_, θ_, z_}] := 
      r^(λ + 1) f[θ]
Laplacian[F[{r, θ, z}], 
      Cylindrical[r, θ, z]]
eq = 
      Simplify[Biharmonic[F[{r, θ, z}], 
          Cylindrical[r, θ, z]]]
fsol = DSolve[eq == 0, 
          f[θ], θ][[1]]

f[θ_] = f[θ] /. fsol; 
    ff =  Simplify[f[θ]]

ϕ = 
      Simplify[ComplexExpand[ff], Element[λ, Reals]]

ϕ = (A1 Cos[(λ + 1) θ] + 
              A2 Sin[(λ + 1) θ] + 
              A3 Cos[(λ - 1) θ] + 
              A4 Sin[(λ - 1) θ]) 
          r^(λ + 1) ;
σr = 
      Simplify[D[ϕ, r]/r + 
          D[ϕ, {θ, 2}]/r^2]
τrθ = 
      Simplify[D[ϕ, θ]/r^2 - 
          D[ϕ, r, θ]/r]
σθ = Simplify[D[ϕ, {r, 2}]]

line1=Coefficient[σθ /. θ -> a, {A1, A2, 
            A3, A4}]/((r^(λ - 1)) λ)[[1]]

line2=Coefficient[σθ /. θ -> -a, {A1, 
            A2, A3, A4}]/((r^(λ - 1)) λ)[[1]]

line3=Coefficient[τrθ /. θ -> a, {A1, A2, 
            A3, A4}]/((r^(λ - 1)) λ)[[1]]

line4=Coefficient[τrθ /. θ -> -a, {A1, 
            A2, A3, A4}]/((r^(λ - 1)) λ)[[1]]

mat = {line1, line2, line3, line4};  MatrixForm[mat]

Det[mat]

eq = Simplify[Det[mat]]

Factor[eq /. Cos[4 a] ->  (1 - 2 (Sin[2 a])^2)  /. 
        Cos[4 a λ] ->  (1 - 
              2 (Sin[2 a λ])^2)]

aa = 
        300 Pi/360;
Plot[{λ , -λ, -Sin[2 aa λ]/
          Sin[2 aa ]}, {λ, 0, 1}, 
      PlotStyle -> {Hue[0.7], Hue[0.3], Hue[1]}]

asymm = 
        Table[{i, λ /. FindRoot[
                  Sin[2 i Pi λ/360] - λ Sin[
                          2 i Pi/360] == 0, {λ, 0.65,  0.25, 
                    1.1}][[1]]}, {i, 220, 
            360}];
  
  
symm1 = 
        Table[{i, λ /. FindRoot[
                  Sin[2 i Pi λ/360] + λ Sin[
                          2 i Pi/360] == 0, {λ, 0.75,  0.25, 
                    1.1}][[1]]}, {i, 180, 
            320}];
symm2 = 
        Table[{i, λ /. FindRoot[
                  Sin[2 i Pi λ/360] + λ Sin[
                          2 i Pi/360] == 0, {λ, 0.5,  0.25, 
                    1.1}][[1]]}, {i, 320, 
            360}];
  
symm = Join[symm1, symm2];
  
MultipleListPlot[symm, asymm]

l1 = {1, 2, 3}
l2 = {4, 5, 6}
l3 = {{l1}, {l2}}