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Static and cinematic behavior of flat rectangular Nexorade. Analytical solution was found using homogenization techniques

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What’s a reciprocal system? 1 2 1. Sketch of a roofing, by Villard de Honnecourt 13th century 2. Drawing of a bridge, by Leonardo da Vinci 16th century Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 2

What’s a nexorade nowadays? 3 4 3. Workshop on Nexorade construction, NIB Salerno Italy, D. Picker and G. Salvatore 4. Graphic 3D representation Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 3

What’s a nexorade nowadays? 5 6 5. Bibracte, sheltering over an archeological site, RFR and TESS 6. 3D representation of the Bibracte structural system Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 4

Homogenization Technique outcomes • Better understanding of structural behaviour • Influence of each parameter on the whole structure • Optimization 5 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Homogenization Technique 7. Just a few bricks 6 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Homogenization Technique 7. Just a few bricks 8. A brick wall 7 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

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 8

Homogenization Technique 10 10. Applying strain on average on the unit cell Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 9

Homogenization Technique for discrete media Unit cell 11. The Nexorade studied and the Unit Cell Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 10

Homogenization Technique outcomes • Better understanding of structural behaviour • Influence of each parameter on the whole structure • Optimization 11 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Nexorade configuration φ =0 φ = φ* φ = 45° a/l = 0 0 ≤ a/l ≤ 0.5 a/l = 0.5 12 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Degenerated Kirchhoff-Love plate model • Only biaxial bending stiffness, linked to mean curvature • Torsion leads to free motion → no stress 13 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Out of Plane Shear and Bending moment 12 13 12. Out of plane bending moment 13. Out of plane shear 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 Shear as function of a/l Bending moment as function of a/l 15 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Out of Plane Stiffness Stiffness as function of engagment ratio a/l. Shear stiffness is never negligible 16 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

Out of Plane FEM Analysis 14 15 16 14. Shear 15. Bending moment 16. Displacement Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 17

FEM validation 17 18 17. Displacement convergence, error as function of the number of unit cells 18. Displacement values comparison, Analytical vs FEM (Abaqus) Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE 18

Conclusion and Outlooks • Good understanding of nexorade stress and displacement fields • Correlation between geometric variables and structural behavior • Other nexor pattern? • In-plane behavior? • Homogenization as a shell? 19 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

THANKS FOR YOUR KIND ATTENTION 20 Investigation of the elastic behavior of reciprocal systems using homogenization techniques Lorenzo GRECO, Arthur LEBÉE, Cyril DOUTHE

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