aerosandbox.structures.legacy.simple_beam_opt_daedalus_calibration#
Simple Beam
A simple 2D beam example, to be integrated later for full aerostructural modeling. TODO do that.
Governing equation for bending: Euler-Bernoulli beam theory.
(E * I * u(x)’’)’’ = q(x)
- where:
E is the elastic modulus
I is the bending moment of inertia
u(x) is the local displacement at x.
q(x) is the force-per-unit-length at x. (In other words, a dirac delta is a point load.)
()’ is a derivative w.r.t. x.
Governing equation for torsion: phi(x)’’ = -T / (G * J)
- where:
phi is the local twist angle
T is the local torque per unit length
G is the local shear modulus
J is the polar moment of inertia
()’ is a derivative w.r.t. x.