PFR - Aerospace Engineering Sciences Senior Design Projects ...

Project Final Report – CUDBF April 30 th , 2009
ASEN 4028: Aerospace Senior Projects
Using the 4 th order integration method on Equation 19 produces the following functions for the
total displacement, displacement slope, moment, and shear force. These can be seen in Equation
20, Equation 21, Equation 22, and Equation 23, respectively. The code for this can be found in
Appendix H.
() = − 0.001
3 + 0.0215 + 0.807 +
2
Equation 20: Shear Force Distribution
() = − 0.001
12 + 0.0215 + 0.807 + +
6
2
Equation 21: Bending Moment Distribution
() = − 0.001
60 + 0.0215
24 + 0.807
6 + 2 + +
Equation 22: Displacement Slope Distribution
() = − 0.001
360 + 0.0215
120 + 0.807
24 + 6 + 2 + +
Equation 23: Displacement Distribution
Applying boundary conditions of a fixed restraint at the wing root and a free end at the wingtip,
the following boundary conditions are produced.
2 = 0; 2 = 0
(0) = 0; (0) = 0
Equation 24: Boundary Conditions for Wing Bending
Using these boundary conditions, the integration constants from the previous equations are
computed in Equation 25.
= 0.001
3 2
= 0.001
12 2
− 0.0215
2 2 − .807 2
− 0.0215
2 2 − .807
2 − 2
= 0; = 0
Equation 25: Constants of Integration
83