2026-09-19T08:40:45Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/879502022-01-13T07:54:01Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Frédo Durand and John A. Ochsendorf.
Shin, Hijung Valentina
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2014-06-13T22:35:39Z
2014-06-13T22:35:39Z
2014
2014
http://hdl.handle.net/1721.1/87950
880417323
Thesis: S.M. in Computer Science and Engineering, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages [41]-44).
This thesis presents novel analysis and visualization methods to explore the equilibrium of masonry structures. Following a previous approach, we model the stability problem as a quadratic program. When a structure is unstable the quadratic program returns a measure of infeasibility. We extend this model to include tensile structures such as cables. Then, we derive a closed-form gradient of stability with respect to geometry modifications, and apply it to the design of structurally sound buildings. In addition, we analyze various properties related to the equilibrium state of structures and visualize the result. We study the sensitivity of equilibrium with respect to block weights, and from that we trace the flow of forces in the structure. Finally, we compare the equilibrium approach to the finite element analysis (FEA) method-the most widely used alternative. We point out the disadvantage of FEA that comes from formulating the contact constraints and propose an improvement based on an iterative constraint relaxation algorithm.
by Hijung Valentina Shin.
S.M. in Computer Science and Engineering
44 pages
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Analysis and visualization of equilibrium in masonry structures
Thesis
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<Abstract>This thesis presents novel analysis and visualization methods to explore the equilibrium of masonry structures. Following a previous approach, we model the stability problem as a quadratic program. When a structure is unstable the quadratic program returns a measure of infeasibility. We extend this model to include tensile structures such as cables. Then, we derive a closed-form gradient of stability with respect to geometry modifications, and apply it to the design of structurally sound buildings. In addition, we analyze various properties related to the equilibrium state of structures and visualize the result. We study the sensitivity of equilibrium with respect to block weights, and from that we trace the flow of forces in the structure. Finally, we compare the equilibrium approach to the finite element analysis (FEA) method-the most widely used alternative. We point out the disadvantage of FEA that comes from formulating the contact constraints and propose an improvement based on an iterative constraint relaxation algorithm.</Abstract>
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