SLIDES-1 - EAS 4210C AIRCRAFT STRUCTURES II Spring 2002 1...

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EAS 4210C
AIRCRAFT STRUCTURES II
Spring 2002

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Introduction
1) Given a structure under load:
■
We wish to compute the deformation and/or stresses in
the beam. One way is:
◆
to solve the differential equation governing the deflection:
✦
Analytical solution is difficult or impossible if q(x) is
arbitrary, the beam is not uniform,or the structure is more
complex.
q(x)
) (
2
2
2
2
x q
dx
y d
EI
dx
d
=









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The same applies to thermal problems
2) Given a continuum in a steady
thermal environment:
■
We wish to compute the temperature distribution and/or
heat flux in the continuum. One way is:
◆
to solve the differential equation governing the
temperature field:
✦
Analytical solution is difficult or impossible if the
boundary conditions are complex, the medium is not
homogeneous, and/or the shape of the domain is
irregular
0 =








∂
∂
∂
∂
+






∂
∂
∂
∂
y
T
k
y x
T
k
x
T
0
q

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And fluid flow
3) Given a fluid flow in plane:
■
We wish to compute the pressure and/or velocity field in
the fluid. One way is:
◆
to solve the three differential equations governing those
fields: (only one is shown below)
✦
Analytical solution is difficult or impossible if the
boundary conditions are complex, the shape of the
domain is irregular, and/or the viscosity is not uniform
0 =
∂
∂
−




