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Abstract(s)
No projeto de qualquer tipo de estrutura, independentemente qual a sua tipologia, a fase de análise estrutural é uma fase primordial que permite determinar os efeitos que os esforços provocam na estrutura, e antecede o processo de dimensionamento. O Método de Elementos Finitos (MEF) tem sido amplamente integrado em diversos programas de análise e dimensionamento estrutural e encontra-se atualmente acessível à generalidade dos projetistas de estruturas. Contudo, na maioria dos programas comercializados o projetista não tem acesso ao código fonte do programa que se encontra a utilizar e, diversas vezes, desconhece as características do modelo utilizado na análise. Igualmente, em determinadas circunstâncias e sem a formação devida, a definição do modelo de análise pode revelar-se complexa e tornar-se numa potencial fonte de erros. A presente dissertação pretende criar um programa através do software Matlab® que permita ao utilizador analisar estruturas reticuladas bidimensionais com ligação contínua ou articulada, através do MEF. Portanto, inicialmente são desenvolvidas e modificadas as formulações matemáticas que permitem estudar os elementos unidimensionais de barra, viga e estrutura de dois nós e três nós. Após a realização destas formulações, procedeu-se à obtenção da solução com auxílio ao programa Matlab®, desenvolvendo-se para isso um programa de análise estrutural que permite ao utilizador estudar estruturas reticuladas bidimensionais. As rotinas desenvolvidas e modificadas no programa Matlab® foram compiladas numa interface gráfica através do programa Matlab® Graphical User Interface Development Environment (GUIDE). Desta forma, o utilizador consegue utilizar a ferramenta desenvolvida de forma mais autónoma e expedita. Adicionalmente, esta aplicação permite ao utilizador escolher qual o tipo de formulação, quadrática ou linear, que pretende utilizar na fase de processamento para obter a solução do problema. A validação do programa consistiu numa verificação de cada um dos elementos formulados, e confrontaram-se os resultados obtidos com os esperados pela Resistência dos Materiais e resultantes de softwares comummente utilizados no mercado. Após a modelação de três problemas modelo para cada uma das formulações realizadas, pode-se aferir o correto funcionamento do programa elaborado, que pode agora ser utilizado de forma fiável e intuitiva para o projeto de estruturas mecânicas.
In the design of any type of structure, regardless of its typology, the structural analysis phase is a primary phase that allows determining the effects that the imposed loads cause on the structure, and precedes the design process. The Finite Element Method (FEM) has been widely integrated into several structural analysis and design programs and is currently accessible to most structural designers. However, in most commercial programs, the designer does not have access to the source code of the program he is using and, several times, he is unaware of the characteristics of the model used in the analysis. Likewise, in certain circumstances and without the necessary training, the definition of the analysis model can prove complex and become a potential source of errors. This dissertation intends to create a program through the Matlab® software that allows the user to analyze two-dimensional reticulated structures with continuous or articulated connections, through the FEM. Therefore, the mathematical formulations that allow to study one-dimensional truss, beam and frame elements of two and three nodes are developed and modified. After performing these formulations, the solution was obtained with the aid of the Matlab® software, developing a structural analysis program that allows the user to study two-dimensional reticulated structures. The developed and modified routines in the Matlab® software were compiled in a graphical interface through the Matlab® GUIDE software. In this way, the user is able to use the developed tool in a more autonomous and expeditious manner. Additionally, this application allows the user to choose which type of formulation, quadratic or linear, he wants to use in the processing phase to obtain the solution to the problem. The program validation consisted of checking each of the formulated elements, and the results obtained were compared with those expected by the Strength of Materials and resulting from commonly used software in the market. After modeling three sample problems for each of the performed formulations, it is possible to assess the correct functioning of the elaborated program, which can now be used in a reliable and intuitive way for the design of mechanical structures.
In the design of any type of structure, regardless of its typology, the structural analysis phase is a primary phase that allows determining the effects that the imposed loads cause on the structure, and precedes the design process. The Finite Element Method (FEM) has been widely integrated into several structural analysis and design programs and is currently accessible to most structural designers. However, in most commercial programs, the designer does not have access to the source code of the program he is using and, several times, he is unaware of the characteristics of the model used in the analysis. Likewise, in certain circumstances and without the necessary training, the definition of the analysis model can prove complex and become a potential source of errors. This dissertation intends to create a program through the Matlab® software that allows the user to analyze two-dimensional reticulated structures with continuous or articulated connections, through the FEM. Therefore, the mathematical formulations that allow to study one-dimensional truss, beam and frame elements of two and three nodes are developed and modified. After performing these formulations, the solution was obtained with the aid of the Matlab® software, developing a structural analysis program that allows the user to study two-dimensional reticulated structures. The developed and modified routines in the Matlab® software were compiled in a graphical interface through the Matlab® GUIDE software. In this way, the user is able to use the developed tool in a more autonomous and expeditious manner. Additionally, this application allows the user to choose which type of formulation, quadratic or linear, he wants to use in the processing phase to obtain the solution to the problem. The program validation consisted of checking each of the formulated elements, and the results obtained were compared with those expected by the Strength of Materials and resulting from commonly used software in the market. After modeling three sample problems for each of the performed formulations, it is possible to assess the correct functioning of the elaborated program, which can now be used in a reliable and intuitive way for the design of mechanical structures.
Description
Keywords
Método de Elementos Finitos Elementos unidimensionais Elemento de barra Elemento de viga Elemento de estrutura Formulação linear e quadrática Funções de interpolação Transformação de coordenadas Matlab® Matlab® GUIDE Interface gráfica FELP Finite Element Method One-dimensional elements Bar element Beam element Frame element Linear and quadratic formulation Interpolation functions Coordinate transformation Graphic interface