On the equilibrium of simplicial masonry structures

ACM Transactions on Graphics

Volumn 32, Issue 4, 2013, Pages

  De Goes, Fernando ^a   Alliez, Pierre ^b   Owhadi, Houman ^a   Desbrun, Mathieu ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b INRIA   (France)

Author keywords

Architectural geometry; Discrete differential geometry; Geometry processing; Orthogonal reciprocal diagram

Indexed keywords

ANALYSIS AND DESIGN; ARCHITECTURAL GEOMETRY; DISCRETE DIFFERENTIAL GEOMETRY; GEOMETRIC PROPERTIES; GEOMETRY PROCESSING; MASONRY STRUCTURES; NUMERICAL HOMOGENIZATION; ORTHOGONAL RECIPROCAL DIAGRAM;

GEOMETRY;

MASONRY MATERIALS;

EID: 84880784518     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/2461912.2461932     Document Type: Article

References (32)

1. ALLIEZ, P., COHEN-STEINER, D., YVINEC, M., AND DESBRUN, M. 2005. Variational tetrahedral meshing. ACM Trans. Graph. 24, 3 (July), 617-625.
2. ANGELILLO, M., BABILIO, E., AND FORTUNATO, A. 2012. Singular stress fields for masonry-like vaults. Continuum Mechanics and Thermodynamics, 1-19.
3. AURENHAMMER, F., HOFFMANN, F., AND ARONOV, B. 1998. Minkowski-type theorems and least-squares clustering. Algorithmica 20, 1, 61-76.
4. BLOCK, P., AND LACHAUER, L. 2011. Closest-fit, compressiononly solutions for free form shells. In IABSE/IASS London Symposium, Int. Assoc. Shell Spatial Structures.
5. BLOCK, P., AND OCHSENDORF, J. 2007. Thrust network analysis: A new methodology for three-dimensional equilibrium. J. Int. Assoc. Shell and Spatial Structures 48, 3, 167-173.
6. BLOCK, P. 2009. Thrust Network Analysis: Exploring Threedimensional Equilibrium. PhD thesis, Department of Architecture, Massachusetts Institute of Technology.
7. CGAL, 2012. Computational Geometry Algorithms Library (release 4.1). http://www.cgal.org.
8. DESBRUN, M., KANSO, E., AND TONG, Y. 2007. Discrete differential forms for computational modeling. In Discrete Differential Geometry, A. Bobenko and P. Schröder, Eds. Springer.
9. DESBRUN, M., DONALDSON, R., AND OWHADI, H. 2013. Modeling across scales: Discrete geometric structures in homogenization and inverse homogenization. In Multiscale analysis and nonlinear dynamics, M. Z. Pesenson, Ed., vol. 8 of Reviews of Nonlinear Dynamics and Complexity. Wiley.
10. FISHER, M., SCHRÖDER, P., DESBRUN, M., AND HOPPE, H. 2007. Design of tangent vector fields. In Proceedings of ACM SIGGRAPH.
11. FOSDICK, R., AND SCHULER, K. 2003. Generalized Airy stress functions. Meccanica 38, 5, 571-578.
12. FRATERNALI, F., ANGELILLO, M., AND FORTUNATO, A. 2002. A lumped stress method for plane elastic problems and the discretecontinuum approximation. International Journal of Solids and Structures 39, 6211-6240.
13. FRATERNALI, F. 2010. A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions. Mechanics Research Communications 37, 2, 198-204.
14. FRATERNALI, F. 2011. A mixed lumped stress-displacement approach to the elastic problem of masonry walls. Mechanics Research Communications 38, 176-180.
15. GIAQUINTA, M., AND GIUSTI, E. 1985. Researches on the equilibrium of masonry structures. Archive for Rational Mechanics and Analysis 88, 359-392.
16. GLICKENSTEIN, D., 2005. Geometric triangulations and discrete Laplacians on manifolds. arXiv.org:math/0508188.
17. GRADY, L. J., AND POLIMENI, J. R. 2010. Discrete Calculus: Applied Analysis on Graphs for Computational Science. Springer.
18. GREEN, A., AND ZERNA, W. 2002. Theoretical Elasticity. Dover.
19. HEYMAN, J. 1966. The stone skeleton. International Journal of Solids and Structures 2, 2, 249-279.
20. MERCAT, C. 2001. Discrete Riemann surfaces and the Ising model. Comm. Math. Phys. 218, 177-216.
21. MÉRIGOT, Q. 2011. A multiscale approach to optimal transport. Computer Graphics Forum 30, 5, 1583-1592.
22. MULLEN, P., MEMARI, P., DE GOES, F., AND DESBRUN, M. 2011. HOT: Hodge-optimized triangulations. ACM Trans. Graph. 30, 4 (July), 103:1-103:12.
23. O'DWYER, D. 1999. Funicular analysis of masonry vaults. Computers & Structures 73, 1-5, 187-197.
24. PREPARATA, F. P., AND SHAMOS, M. I. 1985. Computational Geometry: An Introduction. Springer-Verlag.
25. TONG, Y., ALLIEZ, P., COHEN-STEINER, D., AND DESBRUN, M. 2006. Designing quadrangulations with discrete harmonic forms. In Symposium on Geometry Processing, 201-210.
26. VOUGA, E., HÖBINGER, M., WALLNER, J., AND POTTMANN, H. 2012. Design of self-supporting surfaces. ACM Trans. Graph. 31, 4, 87:1-87:11.
27. WÄCHTER, A., AND BIEGLER, L. T. 2006. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 1, 25-57.
28. WARDETZKY, M., MATHUR, S., KÄLBERER, F., AND GRINSPUN, E. 2007. Discrete Laplace operators: no free lunch. In Symposium on Geometry Processing, 33-37.
29. WHITING, E., OCHSENDORF, J., AND DURAND, F. 2009. Procedural modeling of structurally-sound masonry buildings. ACM Transactions on Graphics 28, 5, 112:1-112:10.
30. WHITING, E., SHIN, H., WANG, R., OCHSENDORF, J., AND DURAND, F. 2012. Structural optimization of 3D masonry buildings. ACM Transactions on Graphics 31, 6, 159:1-159:11.
31. WONG, Y. W., AND PELLEGRINO, S. 2006. Wrinkled membranes Part II: analytical models. Journal of Mechanics of Materials and Structures 1, 25-59.
32. ZAYER, R., ROSSL, C., AND SEIDEL, H.-P. 2005. Discrete tensorial quasi-harmonic maps. In Proceedings of Shape Modeling and Applications, 278-287.