Hi, I need help with this numerical methods question. Please provide detailed workings and/or explanations where possible as I'm trying to understand the methods of tackling these types of questions. Thank you.
Question 4
a) The load acting over the span of the aircraft horizontal stabilizer is uniformly distributed as shown in the figure below:
2L
Wo N/m
Front view
4E1
EI
plane view
]
C
If the span of the horizontal stabilizer is 2L, and the uniformly distributed load is Wo N/m. The stabilizer can be considered to be fixed supported at the root.
The horizontal stabilizer is approximated using a 2-element beam bending model. Both elements have a length of L, and the element cross-sectional property is shown in the figure.
(i) Calculate the equivalent loads acting at nodes A, B, and C respectively.
(ii) Given the element stiffness matrix for the beam element is:
[12 79 -12
79 412 6L
-12 6L 212 L^3]
Analyze and Compute the stiffness matrix for each of the beam elements.
(i) Formulate and assemble the stiffness matrix of the entire horizontal stabilizer.
b) 1. State the Boundary Conditions for this model.
11. Design a suitable numerical procedure for the solution for the deflection and rotation at node 3 (Just provide the procedure, NO actual working is required.)
