Following this query and consumer21 answered, I modified the BCs of the preliminary drawback. The code following bellow.

```
<< NumericalDifferentialEquationAnalysis`;
Wants["NDSolve`FEM`"];
G = Rationalize[6.894745 10^9]
E1 = Rationalize[26.25 G]; E2 = Rationalize[1.49 G]; G12 =
Rationalize[1.04 G]; nu12 = Rationalize[0.28]; nu21 = (E2*nu12)/E1;
t = Rationalize[0.0050 .0254];
Son = {{1/E1, -nu12/E1, 0}, {-nu21/E2, 1/E2, 0}, {0, 0, 1/G12}};
Qon = Inverse[Son];
Q11 = Qon[[1, 1]]; Q12 = Qon[[1, 2]]; Q22 = Qon[[2, 2]]; Q66 =
Qon[[3, 3]];
U1 = (Three Q11 + Three Q22 + 2 Q12 + four Q66)/8; U2 = (Q11 - Q22)/
2; U3 = (Q11 + Q22 - 2 Q12 - four Q66)/
8; U4 = (Q11 + Q22 + 6 Q12 - four Q66)/
8; U5 = (Q11 + Q22 - 2 Q12 + four Q66)/8;
alpha = 45 ([Pi]/180);
a = 1; b = 1; d = a Cos[alpha] + b Sin[alpha];
omega = Rectangle[{0, 0}, {a, b}];
mesh = ToElementMesh[omega, MaxCellMeasure -> 0.001];
u0 = Rationalize[0.01];
angle1 = 10; angle0 = 0;
angles = {{angle0, angle1}, {-angle0, -angle1}, {angle0,
angle1}, {-angle0, -angle1}, {angle0,
angle1}, {-angle0, -angle1}, {-angle0, -angle1}, {angle0,
angle1}, {-angle0, -angle1}, {angle0,
angle1}, {-angle0, -angle1}, {angle0, angle1}};
num = Dimensions[angles][[1]]; h = num*t; pos = Desk[0, num + 1];
pos[[1]] = -h/2;
For[i = 2, i <= num + 1, i++, pos[[i]] = pos[[i - 1]] + t];
[Xi]A = {0, 0, 0, 0, 0};
[Xi]B = {0, 0, 0, 0, 0};
[Xi]D = {0, 0, 0, 0, 0};
For[i = 1, i <= num, i++, T0 = angles[[i, 1]];
T1 = angles[[i, 2]];
func[s_] :=
Simplify@((2/d) (T1 - T0) Sqrt[(s - d/2)^2] + T0) ([Pi]/180);
theta[x_, y_] := alpha + func[x Cos[alpha] + y Sin[alpha]];
zA = pos[[i + 1]] - pos[[i]];
zB = pos[[i + 1]]^2 - pos[[i]]^2;
zD = pos[[i + 1]]^3 - pos[[i]]^3;
V1 = Cos[2 theta[x, y]]; V2 = Sin[2 theta[x, y]];
V3 = Cos[4 theta[x, y]]; V4 = Sin[4 theta[x, y]];
[Xi]a = {1, V1, V2, V3, V4} zA;
[Xi]b = {1, V1, V2, V3, V4} zB;
[Xi]d = {1, V1, V2, V3, V4} zD;
[Xi]A = [Xi]A + [Xi]a;
[Xi]B = [Xi]B + [Xi]b;
[Xi]D = [Xi]D + [Xi]d;];
mU = {{U1, U2, 0, U3, 0}, {U4, 0, 0, -U3, 0}, {U1, -U2, 0, U3, 0}, {0,
0, U2/2, 0, U3}, {0, 0, U2/2, 0, -U3}, {U5, 0, 0, -U3, 0}};
mA = mU.[Xi]A; mB = (mU.[Xi]B)/2; mD = (mU.[Xi]D)/3;
A11[x_, y_] = mA[[1]]; A12[x_, y_] = mA[[2]]; A16[x_, y_] = mA[[4]];
A22[x_, y_] = mA[[3]]; A26[x_, y_] = mA[[5]]; A66[x_, y_] = mA[[6]];
D11[x_, y_] = mD[[1]]; D12[x_, y_] = mD[[2]]; D16[x_, y_] = mD[[4]];
D22[x_, y_] = mD[[3]]; D26[x_, y_] = mD[[5]]; D66[x_, y_] = mD[[6]];
Nx[x_, y_] =
A11[x, y] D[u[x, y], {x, 1}] + A12[x, y] D[v[x, y], {y, 1}] +
A16[x, y] (D[u[x, y], {y, 1}] + D[v[x, y], {x, 1}]);
Ny[x_, y_] =
A12[x, y] D[u[x, y], {x, 1}] + A22[x, y] D[v[x, y], {y, 1}] +
A26[x, y] (D[u[x, y], {y, 1}] + D[v[x, y], {x, 1}]);
Nxy[x_, y_] =
A16[x, y] D[u[x, y], {x, 1}] + A26[x, y] D[v[x, y], {y, 1}] +
A66[x, y] (D[u[x, y], {y, 1}] + D[v[x, y], {x, 1}]);
PDEs = {D[Nx[x, y], {x, 1}] + D[Nxy[x, y], {y, 1}],
D[Ny[x, y], {y, 1}] + D[Nxy[x, y], {x, 1}]};
gammaD = {DirichletCondition[{v[x, y] == u0}, y == 0],
DirichletCondition[{v[x, y] == -u0}, y == b]};
omega = Rectangle[{0, 0}, {a, b}];
mesh = ToElementMesh[omega, MaxCellMeasure -> 0.001];
PDEs = FullSimplify[PDEs];
{U, V} = NDSolveValue[{PDEs == {0, 0}, gammaD,
DirichletCondition[u[x, y] == 0, x == a/2]}, {u,
v}, {x, y} [Element] mesh];
```

Plotting it the answer for U[x,y], it is attainable to see two peaks.

Differentiation of x (`D[U[x, y], {x, 1}]`

) potentiates these peaks as might be seen bellow

These usually are not anticipated outcomes. Would anybody know the rationale of those peaks? I have been tried to refine the mesh (~ 10000 quad components) and these peaks hold taking place. Am I shedding some necessary factor right here?