A review of methods applicable to the study of masonry historical construction, encompassing both classical and advanced ones, is presented. Firstly, the paper offers a discussion on the main challenges posed by historical structures and the desirable conditions that approaches oriented to the modeling and analysis of this type of structures should accomplish. Secondly, the main available methods which are actually used for study masonry historical structures are referred to and discussed. The main available strategies, including limit analysis, simplified methods, FEM macro- or micro-modeling and discrete element methods (DEM) are considered with regard to their realism, computer efficiency, data availability and real applicability to large structures. A set of final considerations are offered on the real possibility of carrying out realistic analysis of complex historic masonry structures. In spite of the modern developments, the study of historical buildings is still facing significant difficulties linked to computational effort, possibility of input data acquisition and limited realism of methods.

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Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches

Vision of 3D printing with concrete — Technical, economic and environmental potentials

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry. Graphical abstractDisplay Omitted HighlightsThis is a survey paper on 'architectural geometry' as a geometric discipline, together with references to real projects.

Architectural Geometry

This paper presents a new methodology for generating compression-only vaulted surfaces and networks. The method finds possible funicular solutions under gravitational loading within a defined envelope. Using projective geometry, duality theory and linear optimization, it provides a graphical and intuitive method, adopting the same advantages of techniques such as graphic statics, but offering a viable extension to fully three-dimensional problems. The proposed method is applicable for the analysis of vaulted historical structures, specifically in unreinforced masonry, as well as the design of new vaulted structures. This paper introduces the method and shows examples of applications in both fields.

/pdf/thrust-network-analysis-a-new-methodology-for-three-32mijmbkg5.pdf

Thrust network analysis : a new methodology for three-dimensional equilibrium

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing.

Quad-Mesh Generation and Processing: A Survey

http://web.mit.edu/masonry/papers/block_cibl_ochs_CAS.pdf

Real-time limit analysis of vaulted masonry buildings

Acknowledgements Contents On architects and engineers Sharing the same spirit Introduction Part 1: Shells for Architecture 1. Exploring shell forms, John Ochsendorf, Philippe Block 2. Shaping forces, Laurent Ney, Sigrid Adriaenssens 3. What is a shell? Chris Williams 4. Physical modelling and form finding, Bill Addis 5. Computational form finding and optimization, Kai-Uwe Bletzinger, Ekkehard Ramm Part 2: Form Finding 6. Force density method, Klaus Linkwitz 7. Thrust network analysis, Philippe Block, Lorenz Lachauer, Matthias Rippmann 8. Dynamic relaxation, Sigrid Adriaenssens, Mike Barnes, Richard Harris, Chris Williams 9. Particle-spring systems, Shajay Bhooshan, Diederik Veenendaal, Philippe Block 10. Comparison of form-finding methods, Diederick Veenendaal, Philippe Block 11. Steering of form, Axel Kilian Part 3: Structural Optimization 12. Nonlinear force density method, Klaus Linkwitz, Diederick Veenendaal 13. Best-fit thrust network analysis, Tom Van Mele, Daniele Panozzo, Olga Sorkine-Hornung, Philippe Block 14. Discrete topology optimization, James N. Richardson, Sigrid Adriaenssens, Rajan Filomeno Coelho, Philippe Bouillard 15. Multi-criteria gridshell optimization, Peter Winslow 16. Eigenshells, Panagiotis Michalatos, Sawako Kaijima 17. Homogenization method, Irmgard Lochner-Aldinger, Axel Schumacher 18. Computational morphogenesis, Alberto Pugnale, Tomas Mendez Echenagucia, Mario Sassone Part 4: Precedents 19. The Multihalle and the British Museum, Chris Williams 20. Felix Candela and Heinz Isler, Maria E. Moreyra Garlock, David P. Billington 21. Structural design of free-curved RC shells, Mutsuro Sasaki The congeniality of architecture and engineering, Patrik Schumacher Appendices: 22. The finite element method in a nutshell, Chris Williams 23. Differential geometry and shell theory, Chris Williams 24. Genetic algorithms for structural design, Rajan Filomeno Coelho, Tomas Mendez Echenagucia, Alberto Pugnale, James N. Richardson 25. Subdivision surfaces, Paul Shepherd Index Bibliography List of Credits List of Projects List of Contributors

Shell structures for architecture : form finding and optimization

https://www.block.arch.ethz.ch/brg/files/2012-ijss-veenendaal-block_1380094819.pdf

An overview and comparison of structural form finding methods for general networks

This dissertation presents Thrust Network Analysis,
a new methodology for generating compression-only vaulted surfaces
and networks. The method finds possible funicular solutions under
gravitational loading within a defined envelope. Using projective
geometry, duality theory and linear optimization, it provides a
graphical and intuitive method, adopting the same advantages of
techniques such as graphic statics, but offering a viable extension
to fully three-dimensional problems. The proposed method is
applicable for the analysis of vaulted historical structures,
specifically in unreinforced masonry, as well as the design of new
vaulted structures. This dissertation introduces the method and
shows examples of applications in both fields. Thrust Network
Analysis, masonry, historic structures, compression-only
structures, limit analysis, equilibrium analysis, funicular design,
form-finding, structural optimization, Gothic vaults, reciprocal
diagrams.

Philippe Block

Papers

Thrust network analysis : a new methodology for three-dimensional equilibrium

Real-time limit analysis of vaulted masonry buildings

Shell structures for architecture : form finding and optimization

An overview and comparison of structural form finding methods for general networks

Thrust Network Analysis : exploring three-dimensional equilibrium