investigation of the elastic behavior of reciprocal systems using homogenization techniques
DESCRIPTION
Static and cinematic behavior of flat rectangular Nexorade. Analytical solution was found using homogenization techniquesTRANSCRIPT
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
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Presenting Author, Another Author(s)
Investigation of the elastic behavior of reciprocal systems using
homogenization techniquesLorenzo GRECO
University of Pisa
Arthur LEBÉELaboratorie Navier, ENPC
Cyril DOUTHEIFSTTARR
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
2
What’s a reciprocal system?
1. Sketch of a roofing, by Villard de Honnecourt 13th century
2. Drawing of a bridge, by Leonardo da Vinci 16th century
1 2
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
3
What’s a nexorade nowadays?
3. Workshop on Nexorade construction, NIB Salerno Italy, D. Picker and G. Salvatore
4. Graphic 3D representation
3 4
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
4
What’s a nexorade nowadays?
5. Bibracte, sheltering over an archeological site, RFR and TESS
6. 3D representation of the Bibracte structural system
5 6
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
5
Homogenization Technique outcomes
• Better understanding of structural behaviour
• Influence of each parameter on the whole structure
• Optimization
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
6
Homogenization Technique
7. Just a few bricks
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
7
Homogenization Technique
7. Just a few bricks
8. A brick wall
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
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Homogenization Technique
7. Just a few bricks
8. A brick wall
9. Homogenized plate describing the average brick wall behaviour
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
9
Homogenization Technique
10. Applying strain on average on the unit cell
10
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
10
Homogenization Technique for discrete media
11. The Nexorade studied and the Unit Cell
Unit cell
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
11
Homogenization Technique outcomes
• Better understanding of structural behaviour
• Influence of each parameter on the whole structure
• Optimization
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
12
Nexorade configuration
φ = 0
a/l = 0
φ = φ*
0 ≤ a/l ≤ 0.5
φ = 45°
a/l = 0.5
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
13
Degenerated Kirchhoff-Love plate model
• Only biaxial bending stiffness, linked to mean curvature
• Torsion leads to free motion → no stress
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
14
Out of Plane Shear and Bending moment
12. Out of plane bending moment
13. Out of plane shear
12 13
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
15
Out of Plane Shear and Bending moment
Shear as function of a/l Bending moment as function of a/l
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
16
Out of Plane Stiffness
Stiffness as function of engagment
ratio a/l.
Shear stiffness is never
negligible
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
17
Out of Plane FEM Analysis
14. Shear
15. Bending moment
16. Displacement
14 1615
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
18
FEM validation
17. Displacement convergence, error as function of the number of unit cells
18. Displacement values comparison, Analytical vs FEM (Abaqus)
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Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
19
Conclusion and Outlooks
• Other nexor pattern?
• In-plane behavior?
• Homogenization as a shell?
• Good understanding of nexorade stress and displacement fields
• Correlation between geometric variables and structural behavior
Investigation of the elastic behavior of reciprocal systems using homogenization techniques
Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE
20
THANKS FOR YOUR KIND ATTENTION