Algorithm Development for Optimization of Arbitrary
Geometry Panels using Curvilinear Stiffeners
Sameer B. Mulani,
*
Davide Locatelli,
†
and Rakesh K. Kapania
‡
Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0203
Innovative manufacturing techniques like Electron Beam Free Form Fabrication (EBF
3
),
Friction Stir Welding (FSW), and Selective Laser Sintering (SLS) are additive in nature
as opposed to subtractive, meaning that the material is deposited wherever necessary on
the contrary to removal of unnecessary material from the structures. These techniques
have created new opportunities and much bigger design space to optimize structures of
complex shapes especially the aerospace vehicles without much material wastage and energy
(Green Technologies). Earlier research has shown that panels with curvilinear stiffeners
may have a reduced weight than panels with straight stiffeners having the same strength
performance (buckling and stress constraints). Fuselage, supersonic and subsonic wing
panels which are curved can be stiffened using curvilinear (alignment) stiffeners. Our
research in supersonic wing optimization using curvilinear spars and ribs has realized that
the panels bounded by these spars and ribs may have 3 to 6 curved edges that created a new
opportunity and complexity in design of curved panels with curvilinear stiffeners. To design
and optimize such panels, a framework is developed which consists of MD-PATRAN, MD-
NASTRAN, VisualDoc and MATLAB. To create the geometry of stiffened curved panels
in the parametric fashion using MD-PATRAN, three approaches are proposed, namely,
1) Bounding-Box Method, 2) Interpolation of the Shell and Manifold Method, and 3)
Interpolation of the Shell and Curve Projection Method. Advantages and disadvantages of
these approaches are discussed, including remedies for some of the limitations. Amongst
these approaches, the last one, Interpolation of the Shell and Curve Projection Method is the
best to create and analyze the arbitrary geometry panel with curvilinear blade-stiffeners.
These approaches’ efficiency and accuracy are compared for flat rectangular panel with
curved edges and cylindrical shell with curved edges during optimization.
Nomenclature
λ
0
Fundamental Buckling Eigenvalue
v Velocity of the Particles
x Position of the Particles, Design Variables
σ
a
Allowable Stress
σ
stif f
Maximum Negative Principal Stress
σ
vm
von Mises Stress
σ
y
Material Yield Stress
b Stiffener Height
BF
0
Buckling Factor
c
1
Global Optimum Trust Parameter
c
1
Local Optimum Trust Parameter
E Young’s Modulus
F
cc
Maximum Allowable Stiffener Stress
p
i
Particle’s Best Position
*
Post Doctoral Fellow, Aerospace and Ocean Engineering, AIAA Senior Member.
†
Research Assistant, Engineering Science and Mechanics, AIAA Student Member.
‡
Mitchell Professor, Aerospace and Ocean Engineering, AIAA Associate Fellow.
1 of 17
American Institute of Aeronautics and Astronautics
51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th
12 - 15 April 2010, Orlando, Florida
AIAA 2010-2674
Copyright © 2010 by Sameer B Mulani. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.