Application of the Finite Element Method Using MARC and Mentat
81
Chapter 8: Aircraft Fuselage Window
Keywords:
2D elasticity, plane stress, symmetry, superposition
Modeling Procedures:
ruled surface, convert, biased mesh
8.1 Problem Statement and Objectives
An aircraft fuselage structure must be capable of withstanding many types of loads, and stress
concentrations near cutouts are of particular concern. In this exercise, internal pressure in a structure
similar to a Lockheed L1011 commercial aircraft fuselage is considered. The objective of the analysis
is to determine the stress state and the factor of safety in a square fuselage panel containing a window
cutout. The geometrical, material, and loading specifications for the panel are given in Figure 8.1.
Geometry:
Material:
2024T3 aluminum alloy
Radius of Curvature: R=100”
Yield Strength: 50 ksi
Skin Wall Thickness: t=0.063”
Modulus of Elasticity: 10.5 Msi
Window Dimensions: a=10”, b=15”
Poisson’s Ratio: 0.33
Window Corner Radius: r=2”
Loading:
Square Section Span Length: L=30”
Internal Pressure: 9.0 psi
Figure 8.1 Geometry, material, and loading specifications for an aircraft fuselage panel with a window cutout.
L
r
b
a
R
t
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Application of the Finite Element Method Using MARC and Mentat
82
8.2 Analysis Assumptions
1.
The analysis model will consider only the fuselage structure with an open cutout. In other
words, the analysis will be performed as if no window is present (yet pressurization is
maintained).
2.
The radiustothickness ratio (R/t) of the fuselage skin is approximately 1,587. Therefore, the
effect of curvature can be ignored in the present analysis.
3.
The spantothickness ratio (L/t) of the fuselage skin is approximately 476. Therefore, the
structure is very thin and a state of plane stress can be assumed.
4.
The panel edges are a sufficient distance from fuselage stiffeners, so very little bending will
occur due to the applied internal pressure load. The effects of bending will thus be neglected.
8.3 Mathematical Idealization
Based on the assumptions above, a 2D plane stress model of the structure will be developed. The
loads can be obtained from cylindrical pressure vessel theory. In other words, the internal pressure
will cause an axial and a circumferential stress in the cylinder, which can be applied at the edges of the
structural section being modeled. The idealized model is the same as in Figure 8.1, except that the
curvature is ignored.
8.4 Finite Element Model
The finite element model of this structure will be developed using 2D plane stress fournoded
quadrilateral finite elements. The present analysis can be greatly simplified by taking advantage of
existing symmetries in the idealized model. Note that both horizontal and vertical mirror planes of
symmetry exist, as shown in Figure 8.2a. The geometry, material properties, and loading conditions
are all symmetric about these two planes. Therefore, the response of the structure (i.e., displacements,
strains, and stresses) will also be symmetric about these two planes. Hence, it is necessary to model
only a quarter of the panel, as shown in Figure 8.2b. The boundary conditions on the symmetry planes
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 Spring '05
 AVERILL
 Finite Element Method, Stress, main menu, Elliptic boundary value problem, Mentat

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