Piecewise rigid displacement (PRD) method: a limit analysis-based approach to detect mechanisms and internal forces through two dual energy criteria

Open access
Date
2020-07Type
- Journal Article
Citations
Cited 14 times in
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Cited 15 times in
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Abstract
This paper proposes an extension of the Piecewise Rigid Displacement (PRD) method based on a new dual linear programming problem that minimises the complementary energy. Before, the PRD method had been applied to solve the kinematical problem for masonry-like structures composed of normal, rigid, no-tension (NRNT) material minimising the total potential energy. Specifically, the PRD method frames this minimum-energy search as a linear programming problem whose solutions are displacements and singular strain fields (cracks). Here, we show that the corresponding dual linear programming problem discretises the minimum of the complementary energy and returns, as solutions, admissible internal stress states compatible with the crack pattern obtained by solving the primal problem. Thus, these two minimum-energy criteria are dually connected, and their combined use allows coupling mechanisms and internal forces with settlements or homogeneous boundary displacements. This allows addressing different mechanical problems: equilibrium and stability of the reference configuration, effects of settlements, and mechanisms due to overloading (e.g. horizontal forces). Since the NRNT material represents the extension to continuum media of Heyman's material model, the PRD method offers an extremely fast, limit analysis-based, displacement approach that allows simultaneously finding mechanisms and compatible internal forces for any boundary condition, loads and geometry. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000426891Publication status
publishedExternal links
Journal / series
Mechanics Research CommunicationsVolume
Pages / Article No.
Publisher
ElsevierSubject
Masonry; Limit analysis; Unilateral contact; Complementary energy; Settlements; Rigid no-tension materialOrganisational unit
03847 - Block, Philippe / Block, Philippe
Funding
178953 - Practical Stability Assessment Strategies for Vaulted Unreinforced Masonry Structures (SNF)
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Show all metadata
Citations
Cited 14 times in
Web of Science
Cited 15 times in
Scopus
ETH Bibliography
yes
Altmetrics