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Journal of Mechanical Design | Volume 134 | Issue 8 | Research Paper
Research Papers

Optimal Cellular Core Topologies for One-Dimensional Morphing Aircraft Structures

[+] Author and Article Information
K. Raymond Olympio

Department of Aerospace Engineering,  Pennsylvania State University, 229 Hammond Building, University Park, PA 16802Olympio.raymond@gmail.com

Farhan Gandhi

Department of Mechanical, Aerospace, and Nuclear Engineering,  Rensselaer Polytechnic Institute, 110 8th Street, Jonsson Engineering Center, Troy, NY 12180

J. Mech. Des 134(8), 081005 (Jul 24, 2012) (10 pages) doi:10.1115/1.4007087 History: Received September 01, 2011; Revised June 12, 2012; Published July 24, 2012; Online July 24, 2012
Article
References
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Citing Articles

Unlike a conventional aircraft’s wing, a morphing aircraft’s wing could undergo large deformations in order to fly efficiently. This requires a wing’s skin meeting conflicting requirements such as large deformation capability to allow morphing of the underlying structure and high flexural stiffness to maintain the airfoil shape. In this paper, the design of composite skins with a cellular core is considered for the particular case of one-dimensional morphing. Cellular core topologies are calculated using a multi-objective genetic algorithm coupled with a local search optimizer. Morphological filtering is used to remove small features in the topology. As a multi-objective problem, no single solution emerges as the clear best solution because of conflicting objectives. However, the solutions found help guide the design of cellular-based morphing skins. A design is selected from the set of solutions obtained, and a cellular core under combined in-plane morphing and out-of-plane loading is examined with respect to the local stresses, the energy of deformation and the core’s out-of-plane deformation to validate the approach used.
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References

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Figures

Grahic Jump Location
+Determination of the clusters. (a) Only elements in grey are considered neighbors of the element in black and (b) connectivity analysis process.
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Determination of the clusters. (a) Only elements in grey are considered neighbors of the element in black and (b) connectivity analysis process.
Figure 2

Determination of the clusters. (a) Only elements in grey are considered neighbors of the element in black and (b) connectivity analysis process.

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+Boundary conditions applied to the model. (a) Compliant structure with periodic unit cells and (b) quarter of periodic unit.
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Boundary conditions applied to the model. (a) Compliant structure with periodic unit cells and (b) quarter of periodic unit.
Figure 1

Boundary conditions applied to the model. (a) Compliant structure with periodic unit cells and (b) quarter of periodic unit.

Grahic Jump Location
+Illustration of the open filter and close filter
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Illustration of the open filter and close filter
Figure 3

Illustration of the open filter and close filter

Grahic Jump Location
+Example of weights for a two-dimensional problem
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Example of weights for a two-dimensional problem
Figure 4

Example of weights for a two-dimensional problem

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+Comparison of objectives’ values obtained with a linear and a nonlinear FEA (group 1: ×, group 2: □, group 3: ○). (a) Maximum local equivalent strains with linear and nonlinear FEA and (b) strain energy in deformed configuration with linear and nonlinear FEA.
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Comparison of objectives’ values obtained with a linear and a nonlinear FEA (group 1: ×, group 2: □, group 3: ○). (a) Maximum local equivalent strains with linear and nonlinear FEA and (b) strain energy in deformed configuration with linear and nonlinear FEA.
Figure 8

Comparison of objectives’ values obtained with a linear and a nonlinear FEA (group 1: ×, group 2: □, group 3: ○). (a) Maximum local equivalent strains with linear and nonlinear FEA and (b) strain energy in deformed configuration with linear and nonlinear FEA.

Grahic Jump Location
+Selected solution
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Selected solution
Figure 9

Selected solution

Grahic Jump Location
+Effect of the number of cells on the nondimensionalized transverse displacement, δ¯, for a 0.2 m × 0.2 m × 0.01 m panel under an out-of-plane pressure
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Effect of the number of cells on the nondimensionalized transverse displacement, δ¯, for a 0.2 m × 0.2 m × 0.01 m panel under an out-of-plane pressure
Figure 10

Effect of the number of cells on the nondimensionalized transverse displacement, δ¯, for a 0.2 m × 0.2 m × 0.01 m panel under an out-of-plane pressure

Grahic Jump Location
+Deformed shape and equivalent Von Mises strain contours for 33% of global strain with linear or nonlinear deformation. (a) Von Mises strain distribution with a linear deformation, (b) Von Mises strain distribution with a nonlinear extension (ɛmorph  = 33%), and (c) Von Mises strain distribution with a nonlinear compression (ɛmorph  = −21%).
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Deformed shape and equivalent Von Mises strain contours for 33% of global strain with linear or nonlinear deformation. (a) Von Mises strain distribution with a linear deformation, (b) Von Mises strain distribution with a nonlinear extension (ɛmorph  = 33%), and (c) Von Mises strain distribution with a nonlinear compression (ɛmorph  = −21%).
Figure 11

Deformed shape and equivalent Von Mises strain contours for 33% of global strain with linear or nonlinear deformation. (a) Von Mises strain distribution with a linear deformation, (b) Von Mises strain distribution with a nonlinear extension (ɛmorph  = 33%), and (c) Von Mises strain distribution with a nonlinear compression (ɛmorph  = −21%).

Grahic Jump Location
+Influence of the applied pressure and morphing strain (20 × 20 cells). (a) Nondimensionalized out of plane displacement, δ¯, for p0  = 9500 Pa, (b) strain ratio, LGS, and (c) equivalent nondimensionalized stiffness, Emorph.
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Influence of the applied pressure and morphing strain (20 × 20 cells). (a) Nondimensionalized out of plane displacement, δ¯, for p0  = 9500 Pa, (b) strain ratio, LGS, and (c) equivalent nondimensionalized stiffness, Emorph.
Figure 12

Influence of the applied pressure and morphing strain (20 × 20 cells). (a) Nondimensionalized out of plane displacement, δ¯, for p0  = 9500 Pa, (b) strain ratio, LGS, and (c) equivalent nondimensionalized stiffness, Emorph.

Grahic Jump Location
+Flow chart describing the hybrid multi-objective algorithm. The global search block corresponds to the ɛ-NSGA2 algorithm for one single run.
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Flow chart describing the hybrid multi-objective algorithm. The global search block corresponds to the ɛ-NSGA2 algorithm for one single run.
Figure 5

Flow chart describing the hybrid multi-objective algorithm. The global search block corresponds to the ɛ-NSGA2 algorithm for one single run.

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+Triangular scatter plot matrix showing solutions located near the Pareto front of the 1D morphing problem
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Triangular scatter plot matrix showing solutions located near the Pareto front of the 1D morphing problem
Figure 6

Triangular scatter plot matrix showing solutions located near the Pareto front of the 1D morphing problem

Grahic Jump Location
+Linear solutions for the topology optimization of a cellular structure for 1D morphing
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Linear solutions for the topology optimization of a cellular structure for 1D morphing
Figure 7

Linear solutions for the topology optimization of a cellular structure for 1D morphing

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