Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

Probabilistic maintenance and optimization strategies for deteriorating civil infrastructures

In developed countries, civil infrastructures are one of the most significant investments of governments, corporations, and individuals. Among these, transportation infrastructures, including highways, bridges, airports, and ports, are of huge importance, both economical and social. Most developed countries have built a fairly complete network of highways to fit their needs. As a result, the required investment in building new highways has diminished during the last decade, and should be further reduced in the following years. On the other hand, significant structural deteriorations have been detected in transportation networks, and a huge investment is necessary to keep these infrastructures safe and serviceable. Due to the significant importance of bridges in the serviceability of highway networks, maintenance of these structures plays a major role. In this paper, recent progress in probabilistic maintenance and optimization strategies for deteriorating civil infrastructures with emphasis on bridges is summarized. A novel model including interaction between structural safety analysis,through the safety index, and visual inspections and non destructive tests, through the condition index, is presented. Single objective optimization techniques leading to maintenance strategies associated with minimum expected cumulative cost and acceptable levels of condition and safety are presented. Furthermore, multi-objective optimization is used to simultaneously consider several performance indicators such as safety, condition, and cumulative cost. Realistic examples of the application of some of these techniques and strategies are also presented.

Probabilistic models for mechanical properties of prestressing strands

This study focus on the probabilistic modelling of mechanical properties of prestressing strands based on data collected from tensile tests carried out in Laboratório Nacional de Engenharia Civil (LNEC), Portugal, for certification purposes, and covers a period of about 9 years of production. The strands studied were produced by six manufacturers from four countries, namely Portugal, Spain, Italy and Thailand. Variability of the most important mechanicalproperties is examined and the results are compared with the recommendations of the ProbabilisticModel Code, as well as the Eurocodes and earlier studies. The obtained results show a very low variability which, of course, benefits structural safety. Based on those results, probabilistic modelsfor the most important mechanical properties of prestressing strands are proposed.

Probabilistic constraint reasoning

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Informática, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Probabilistic constraint reasoning with Monte Carlo integration to robot localization

This work studies the combination of safe and probabilistic reasoning through the hybridization of Monte Carlo integration techniques with continuous constraint programming. In continuous constraint programming there are variables ranging over continuous domains (represented as intervals) together with constraints over them (relations between variables) and the goal is to find values for those variables that satisfy all the constraints (consistent scenarios). Constraint programming “branch-and-prune” algorithms produce safe enclosures of all consistent scenarios. Special proposed algorithms for probabilistic constraint reasoning compute the probability of sets of consistent scenarios which imply the calculation of an integral over these sets (quadrature). In this work we propose to extend the “branch-and-prune” algorithms with Monte Carlo integration techniques to compute such probabilities. This approach can be useful in robotics for localization problems. Traditional approaches are based on probabilistic techniques that search the most likely scenario, which may not satisfy the model constraints. We show how to apply our approach in order to cope with this problem and provide functionality in real time.

EFFECT – Efficient finite element code

The theme of this dissertation is the finite element method applied to mechanical structures. A new finite element program is developed that, besides executing different types of structural analysis, also allows the calculation of the derivatives of structural performances using the continuum method of design sensitivities analysis, with the purpose of allowing, in combination with the mathematical programming algorithms found in the commercial software MATLAB, to solve structural optimization problems. The program is called EFFECT – Efficient Finite Element Code. The object-oriented programming paradigm and specifically the C ++ programming language are used for program development. The main objective of this dissertation is to design EFFECT so that it can constitute, in this stage of development, the foundation for a program with analysis capacities similar to other open source finite element programs. In this first stage, 6 elements are implemented for linear analysis: 2-dimensional truss (Truss2D), 3-dimensional truss (Truss3D), 2-dimensional beam (Beam2D), 3-dimensional beam (Beam3D), triangular shell element (Shell3Node) and quadrilateral shell element (Shell4Node). The shell elements combine two distinct elements, one for simulating the membrane behavior and the other to simulate the plate bending behavior. The non-linear analysis capability is also developed, combining the corotational formulation with the Newton-Raphson iterative method, but at this stage is only avaiable to solve problems modeled with Beam2D elements subject to large displacements and rotations, called nonlinear geometric problems. The design sensitivity analysis capability is implemented in two elements, Truss2D and Beam2D, where are included the procedures and the analytic expressions for calculating derivatives of displacements, stress and volume performances with respect to 5 different design variables types. Finally, a set of test examples were created to validate the accuracy and consistency of the result obtained from EFFECT, by comparing them with results published in the literature or obtained with the ANSYS commercial finite element code.