Orientador: Marco Lucio Bittencourt / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-14T20:43:50Z (GMT). No. of bitstreams: 1 Miano_MarianaGodoyVazquez_D.pdf: 9321053 bytes, checksum: db1fe6759933884432523889d754a105 (MD5) Previous issue date: 2009 / Resumo: Os Métodos de Elementos Finitos de Alta Ordem tem sido aplicados com sucesso em problemas de Mecânica dos Fluidos e Eletromagnetismo por apresentar uma taxa de convergência exponencial para problemas com solução ao polinomial. No entanto, devido ao uso de funções de interpolação de alta ordem, as matrizes dos elementos são mais densas. Este trabalho apresenta uma formulação ao que permite obter matrizes de rigidez de quadrados e hexaedros altamente esparsas para Problemas de Poisson. Para isso, utiliza-se a equivalência da solução de problemas de projeção unidimensionais que envolvem as matrizes de massa, mista e rigidez. Mostra-se que as matrizes de quadrados e hexaedros podem ser obtidas pela combinação ou tensorização dessas matrizes unidimensionais. A matriz de massa unidimensional que compõe a formulação das matrizes de rigidez de quadrados e hexaedros é densa e pode ser substituída pela matriz de rigidez unidimensional que se mostra bastante esparsa com as funções de base utilizadas no trabalho. A formulação é validada para quadrados e hexaedros locais e estendida para malhas não distorcidas desses mesmos elementos. Erros de aproximação da solução, esparsidade das matrizes de rigidez globais e tempo de execução são apresentados. / Abstract: High-order Finite Element Methods have been applied with success to problems of Fluid Dynamics and Electromagnetism. The main feature of these methods is to present an exponential convergence rate for problems with polinomial solution. However, due to the use of high-order interpolation functions, the elemental matrices are denser. This work shows a mathematical formulation, with tensorization concepts applied to the base functions that make up the matricial system matrices which will enable to write uniformly the systems resulting from the application of mass, mix and stiffness matrices. This possibility arises from the proposed formulation, which makes the solution vector equal to the three systems. Consequently, the 1D array mass, usually dense, that makes up the formulation of the rigid 2D and 3D matrices, in squares and hexahedra, may be replaced by the stiffness matrix 1D, which shows itself very sparse related to the base functions used in this work. The formulation is validated to quadratic and hexahedral elements and it is extended to non-distorted meshes of the same elements in the Poisson problems resolution. Approximation errors in solution, sparsity of the global stiffness and run time are also observed. / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

PIPE5 is a two-dimensional finite element analysis program for buried structure analysis. The program has gone through several changes over the years. Some of the features that were added in the latest revision are stress stiffening, corotational formulation, bandwidth minimization, residual monitoring, and dynamic memory allocation. Some parts of the program were also rewritten to make them clearer and improve their performance. After the modifications several comparisons were made to other programs and earlier versions of the program to test the accuracy of the program in its latest form.

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This paper describes the design methodology of a cast magnesium subframe of a Subaru BRZ using finite element analysis in which the design objective was light-weighting. A simulation based design using Solidworks and ABAQUS was experimentally validated. The final design was developed by optimizing weight and the geometry through multiple iterations of finite element analysis. The fundamentals of this computational design process were to create a way to develop a working physical prototype. Once the design was completed, it was sand cast using an AZ91 magnesium alloy. Experimental validation was performed to confirm the computational results. Through this simulation based design process, the modified subframe weighed 40% less than the original weight, while remaining as strong as the stock subframe.

The study presented attempts to prove the concept that mechanical changes in the structure of a bone can be predicted for a specific exercise by a subject specific model created from CT data, MRI data, EMG data, and a physiologic FE model. Previous work generated a subject specific FE model of a femur via CT and MRI data as well as created a set of subject specific biomechanical muscle forces that are required to perform a single leg extension exercise. The FE model and muscle forces were implemented into a single leg extension FE code (ABAQUS) along with a specialized bone remodeling UMAT. The UMAT updated the mechanical properties of the femur via a damage-repair bone remodeling algorithm. The single leg extension FE code was verified by applying walking loads to the femur and allowing the system to equilibrate. The results were used to apply the appropriate walking loads to the final FE simulation for the single leg extension exercise. The final FE simulation included applying the single leg extension loads over a one year period and plotting the change in porosity at various regions of the femoral neck. Although only two regions were found to generate valid results, the data seemed counterintuitive to Wolff’s Law which states that bone adaptation is promoted when the material is stressed. The model was successful in creating a subject specific model that is capable of predicting changes in the mechanical properties of bone. However, in order to generate valid FE model results, further understanding of the bone remodeling process and application via a FE model is required.

No / Modern manufacturing involves multiple stages of complex process chains where Finite Element Analysis is frequently used as a simulation method on a discretized mesh to provide an accurate estimation of factors such as stresses, strains, and displacements. The choice of the most suitable element type and density is dependent on the individual manufacturing process or treatment applied at each stage of the process chain. To map between unalike Finite Element meshes, differing in density and/or element type, an Octree spatial index was evaluated as a solution for highly performant mapping. Compared to existing solutions, the Octree spatial index introduces parallelism within index creation and provides a strategy to perform the most complex interpolation technique, Element Shape Function, in a more computationally efficient manner.

This thesis focuses on the development of a short-term, operationally stable finite element-based simulation of a mechanical watch lever escapement. This was accomplished in four steps: by choosing a reference escapement based on the needs of the study, by executing a reverse engineering methodology to create a lever escapement in computer-aided design (CAD) software, by capturing experimental data from the reference escapement via custom- built apparatus and then reconciling this data with an analytical model, and by using the knowledge gained from these efforts to develop an implicit dynamic simulation of a lever escapement that aimed to achieve performance metrics defined by watchmaking sources. The final version of the simulated lever escapement was able to meet two of the three performance goals defined for the study. The simulation met the primary performance goal by achieving stable operation for two seconds. During this window of stability, the simulated lever escapement met the secondary performance goal of the study by achieving timing performance metrics defined by watchmaking sources. Unfortunately, the tertiary performance goal was not met as the balance amplitude of the final simulation was outside of the target range by 5.23% when compared against the lower bound. Although the balance amplitude error of the simulated escapement would be indicative of a mechanism that needs servicing, its performance during the stability period was assessed to be representative of a functional lever escapement and therefore, its dynamics and sensitivities were explored and presented. / Master of Science / Mechanical watches rely on physics to keep accurate time. The time regulation mechanism within a mechanical watch is called an escapement, and the most widely used escapement design adopted by watchmakers is the lever escapement. While prior attempts have been made to simulate the physics that these mechanisms use to keep accurate time, achieving stable operating performance in a complete lever escapement simulation remains elusive in published studies. The examination of a stable, simulated lever escapement could reveal new insights into these mechanisms by reducing the impact of transient phenomena. This thesis focuses on the development of a short-term, operationally stable simulation of a lever escapement mechanism. This was achieved by developing a model of a real-world lever escapement, by capturing experimental data to improve the model, and then by applying the knowledge gained from these efforts to create a dynamic simulation in Abaqus/CAE. The final simulation was able to meet two of the three performance goals defined for the study, which proved that it is possible to create a simulation of a lever escapement. Furthermore, the study revealed unexpected phenomena that may be present in real-world lever escapements and may affect their performance.

U-splines are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). A spline is a piecewise-defined function that satisfies continuity constraints between adjacent cells in a mesh. U-splines differ from existing spline constructions, such as Non-Uniform Rational B-splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local variation in cell size, polynomial degree, and smoothness simultaneously over more varied mesh configurations. Mixed cell types (e.g., triangle and tetrahedron and quadrilateral and hexahedral cells in the same mesh) and T-junctions are also supported. The U-spline construction is presented for curves, surfaces, and volumes with higher dimensional generalizations possible. A set of requirements are given to ensure that the U-spline basis is positive, forms a partition of unity, is complete, and is locally linearly independent.

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