Numerical double integrals along discontinuous surfaces

[zmall88]

I posted this in the aerospace engineering forum but I think it may get more replies here:

I've been trying to compute the bending-torsion coupling constants for a wing, B₁, B₂ and B₃. The expression for this is

[itex]
\begin{bmatrix} B_1 \\ B_2 \\ B_3 \end{bmatrix} = \iint (y^2 + z^2)\begin{bmatrix} y^2 + z^2 \\ z \\ y \end{bmatrix}dydyz
[/itex]

where x is in along the wingspan direction, y is along chordwise direction and z is perp. to both.

Question is: how to evaluate this integral?

I have z as a series of points (airfoil shape), where at every y, there are two z values (upper and lower surfaces).

I'm not sure this is in the correct forum or not...

 

[jvicens]

Thank you for posting your question here. I am a scientist with expertise in aerospace engineering and I would be happy to help you with your computation.

To evaluate the integral for the bending-torsion coupling constants, you will need to use numerical methods such as the trapezoidal rule or Simpson's rule. These methods involve breaking up the integral into smaller intervals and approximating the function within each interval using a polynomial. The results from each interval are then combined to give an overall approximation of the integral.

In your case, since z is a series of points, you will need to first interpolate the points to obtain a continuous function for z. Then, you can use the numerical methods to evaluate the integral for each interval along the y-axis and then combine the results to obtain the final values for B1, B2, and B3.

I hope this helps. If you have any further questions, please feel free to ask. Best of luck with your computation!