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Limit Analysis of masonry structures as an unilateral contact problem: resolution by Monte Carlo Method
Áreas de investigación
  • Ingeniería civil y arquitectura
Tema de comunicación admitido Safety assessment of the historic masonry structures is an open problem. The material is hetero-geneous and anisotropic, the previous state of stress is hard to know and the boundary conditions are uncertain. In the early 50's it was proven that limit analysis was applicable to this kind of structures, being considered a suitable tool since then. In cases where no slip occurs the application of the standard limit analysis theorems constitutes an excellent tool for its simplicity and robustness. It is not necessary to know the actual stresses state. It is enough to find any equilibrium solution wich satisfy limit constraints of the material, since we are certain that this load will be equal to or less than the actual load of the onset of col-lapse. Furthermore this load for the onset of collapse is unique (uniqueness theorem), and it can be obtained as the optimal from any of two mathematical convex duals programs However, if the mechanisms of the onset of collapse involve sliding, any solution must satisfy both static and kinematic constraints, and also a special kind of disjunctive constraints linking the previous ones, which can be formulated as complementarity constraints. In the latter case, it is not guaranted the existence of a single solution, so it is necessary to look for other ways to treat the uncertainty associated with its multiplicity. In recent years, research has been focused on finding an absolute minimum below which collapse is impossible. This method is easy to set from the mathematical point of view, but computation-ally intractable. This is due to the complementarity constraints (1), which are neither convex nor smooth. (1) The computational complexity of the resulting decision problem is "Not-deterministic Polyno-mial-complete" (NP-complete), and the corresponding global optimization problem is NP-hard. Furthermore, until a minimum or maximum principle has not be demonstrated, it is questionable that effort expended in approximating this minimum is justified. The purpose of this paper is to find the frequency distribution of the load factor, for all possible solutions of the onset of collapse, on a simple example, and taking advantage of the special char-acteristics of complementarity constraints, which written in bilinear form are (2) (2) For this pourpose, a Monte Carlo sampling of solutions is performed [1] using a contrast method "exact computation of polytopes" [2]. The ultimate goal is to determine the extent to which the search of the global minimum is justi-fied, and to propose an alternative approach to safety assessment based on probabilities. The frequency distributions for the case being studied show that both the maximum and the minimum load factors are very infrequent, especially as the contact gets more perfect and more continuous. The results indicates the interest of further developing the proposed new method.
Nombre congreso
IInd International Congress on Mechanical models in structural engineering
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Esta actividad pertenece a memorias de investigación
  • Autor: Fernando Magdalena Layos (UPM)
  • Autor: Jose Ignacio Hernando Garcia (UPM)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Departamento: Construcciones Arquitectónicas y su Control
  • Departamento: Estructuras de Edificación
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