Piecewise rigid displacement (PRD) method: a limit analysis-based approach to detect mechanisms and internal forces through two dual energy criteria. (July 2020)

• Record Type: Journal Article
• Authors: Iannuzzo, Antonino; Van Mele, Tom; Block, Philippe
• Is Part Of: Mechanics research communications. Volume 107(2020)
• Publication Date: 2020-07
• Subjects: Masonry -- Limit analysis -- Unilateral contact -- Complementary energy -- Settlements -- Rigid no-tension material; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2020.103557
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: Extension of the PRD method to account for internal forces in masonry structures. Minimum of the complementary energy to detect internal stress states. Two dual linear programming problems to couple mechanisms and internal forces. Infinite admissible internal stress states on the initial perfect configuration. PRD analyses of a buttressed arch and effects of settlements on a gothic cathedral. 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.