Aplicação da metodologia numérica “fast bounds crack” para uma estimativa eficiente da evolução do tamanho de trinca

A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".

Metodologia de ensino do conceito de função exponencial à luz da teoria das situações didáticas

This essay presents a proposal on methodology over the mathematical object Exponential Function which enables the development of interpretative and creative skills with potential meaning to the students starting from a didactic sequence structured on the light of The Theory of Didactic Situations from Guy Brousseau and, from the Records of Semiotic Representation of Duval, providing interactions among the students, the teacher and the environment of cooperative learning where the students feel free to express their own ideas as well as to suggest their own approaches. The methodology presented has been developed according to the students first knowledge, valuing their different ways of registering, which have such an important role during the teaching and learning processes. The proposal has been applied to the students from the first year of high school of Colégio Estadual José de Anchieta Ensino Fundamental e Médio, located in a town called Dois Vizinhos –Paraná. In order to the development of the research the methodological tool Didactic Engineering Artigue which consists in a methodology developed only to the research with didactic situations. The main goal has been reached at first, which was to work on the conceptual part of the Exponential Function, the relation of dependence and its main characteristic so that the variable part is in the exponent. Moreover with no imposition but starting from suitable didactic situations, the students were able to realize that they could solve the problems which involve the exponential function and furthermore create new problems (according to their universe) modeled by this kind of function. Its believed that the methodology based on the theory of didactic situations, analysis of students registers, observation on mistakes and obstacles as well as reflections over the aspects of the didactic contract are of fundamental importance to the teaching practice and determinant during the teaching-learning process.

Programa pró-equidade de gênero e raça da Prefeitura Municipal de Curitiba: estratégia para superar a divisão sexual de trabalho em uma instituição pública?

The objective of this study was to analyze if the pro equity program of gender and race in the PMC, changed the perception of the servants on the conception of sexual division of labor. The sexual division of labor is the concept that allows identifying and understanding the hierarchical relations (principal of hierarchization) based on the attribution of social and economic value most male occupations in relation female, besides that, considerers the female work‟s secondary and her salary supplement to the family income. And the principle of separation identifying the places occupies by man and woman in the institution (productive, reproductive, and domestic work) agreeing with the historical and social construction that associates woman to occupational sectors like “mastertship”, nursering and social assistance, considered an extension of the family functions like taking care and family affections. And the man is associate to engineer, technology information and occupations related to exact science all professions associate to reason, creating a bias of gender in labor relations. To identify possible inequalities of gender in the work ambiance, I have compared the initial basic duration of some careers, the ascension process to higher positions and the salary that both servants and servers in the PMC. Was also investigated the perception of implements and beneficiaries of the program, over the sexual labor division. The methodology used for conduct the investigation was the qualitative research interpretive character using the structured and semi structured interviewed as instruments of data collect. The interview was divided in two groups, to follow: a) implements of pro-equity program of gender and race and b) professors and engineers beneficiaries. The analyzes of documents provided by the Secretaria de Politícas para as Mulheres da Presidência da República and by the PMC complemented the investigative path of this research. Bring as result a perception of beneficiaries servants and implementing on a policy which provides for cultural changes in the institution and in the management of people. It should be noted that the program foresees that in its objectives identify the discriminatory relations of race, sexual orientation, generation and disable person who were not examined in this study. Factor that enables the continuation of the investigation process and is a suggestion for a future research.