Method of optimizing stiffened panels under stress
View Patent ↗The subject of the disclosed embodiments is a method of optimizing stiffened panels under stress. In particular, the method makes it possible to determine the stress distribution in stiffened panels with postbuckling taken into account. The method proposed is a coupling between an overall, linear stress calculation approach, based on strength-of-materials results, and a local, nonlinear approach for the behavior of the stiffened panel. The disclosed embodiments fall within the field of aeronautical design, at the pilot study stage in the definition of a civil transport airplane of conventional architecture.
1. Method of optimizing the design of stiffened panels intended for the fuselage of an aircraft ( 5 ) under load, said fuselage being divided up into a set of rings ( 1 ), each ring being decomposed into subsystems ( 2 ), each subsystem being composed of a stiffener ( 3 ) and a skin portion ( 4 ) to which said stiffener is fastened, said subsystem ( 2 ) being subjected to a combined loading of compression and shear stress, characterized in that said method comprises the following successive steps:
a) the local characteristics of the ith subsystem in the initial state, corresponding to a state with no buckling, are determined;
b) the initial overall characteristics of the ring are determined, namely the initial offset of its neutral bending axis ΔZ 0 , its static moment [EW] 0 and its flexural rigidity [EI] 0 are determined from the local characteristics of the ith subsystem;
c) the following are determined in an iterative loop and each iteration n:
the working local characteristics of the subsystem taking into account the loss of rigidity due to buckling, and
the new overall characteristics of the ring, namely its offset [ΔZ 0 ] n , its flexural rigidity [EI] n , and its static moment [EW] n , the convergence of the iterative loop being obtained if the new offset is below a threshold;
d) the final stress distribution in the subsystem is determined;
e) the safety margins are determined from the final stress distribution in the subsystem taking postbuckling into account; and
f) the mass function of the subsystem is minimized while respecting the safety margins.
2. Method according to claim 1 , characterized in that step f) uses an algorithm based on the gradient of a functional for minimizing the mass of the ring.
3. Method according to claim 1 , characterized in that step f) uses a genetic algorithm for minimizing the mass of the ring.
4. Method according to claim 1 , characterized in that the local characteristics of the ith subsystem are the following:
cross section of the skin;
cross section of the stiffener;
Young's modulus;
initial dimension of the center of gravity;
flexural rigidity;
static moment;
critical stress for blistering in compression; and
critical stress for folding in pure shear.
5. Method according to claim 1 , characterized in that the working characteristics of the ith subsystem are the following:
working width
(
c
1
)
n
=
(
c
i
)
n
=
b
i
2
(
σ
blist
i
)
n
(
σ
max
)
n
;
and
working cross section (S i ) n of the skin.
6. Method according to claim 1 , characterized in that the subsystem is defined by two types of variables:
quantitative variables which are geometric variables; and
qualitative variables.
7. Method according to claim 1 , characterized in that said method uses a thickness determined by equivalence corresponding to:
e
equi
=
e
panel
σ
blist
σ
b
.
8. Method according to claim 1 , characterized in that said threshold is set at 1% of the radius of curvature of the stiffened panel.
9. Stiffened panel produced on the basis of the design parameters optimized by said method according to claim 1 .
10. Panel according to claim 9 , characterized in that said panel is a composite panel.
11. Use of said composite panel produced according to claim 10 for equipping an aircraft.