Análise dinâmica de estruturas periódicas utilizando uma abordagem de propagação de ondas e técnicas de sub-estruturação

Orientadores: José Roberto de França Arruda, Jean-Mathieu MencikTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Nesta tese de doutorado, o método dos elementos finitos ondulatórios é utilizado para cálculo da resposta harmônica de sistemas mecânicos envolvendo estruturas com periodicidade unidimensional, i.e., estruturas compostas por subestruturas idênticas arranjadas ao longo de uma direção. Tais sistemas mecânicos podem ser complexos e são comumente encontrados em aplicações de engenharia como, por exemplo, nas fuselagens de aviões. A primeira parte da tese é dedicada ao cálculo das ondas que se propagam ao longo dessas estruturas. Uma breve revisão da literatura sobre as formulações disponíveis para o problema de autovalor associado ao método dos elementos finitos ondulatórios é apresentada, assim como um estudo dos erros numéricos induzidos por estes problemas de autovalor no caso de um guia de ondas sólido. Na segunda parte desta tese, modelagens de superelementos para estruturas periódicas são propostas. Neste contexto, matrizes de rigidez dinâmica e de receptância ou flexibilidade de estruturas periódicas são expressas a partir dos modos de onda. Comparadas às matrizes de rigidez dinâmica e receptância obtidas pelo método dos elementos finitos convencional, as matrizes baseadas no método dos elementos finitos ondulatórios são calculadas de forma bastante rápida e sem perda de acuracidade. Ademais, uma estratégia eficiente de redução de ordem de modelo é apresentada. Comparada às formulações que utilizam a base completa de ondas, esta estratégia proporciona redução do tempo computacional requerido para cálculo da resposta forçada de estruturas periódicas. De fato, é mostrado que elementos espectrais numéricos de alta ordem podem ser construídos a partir do método dos elementos finitos ondulatórios. Isto constitui uma alternativa ao método dos elementos espectrais convencional, cuja utilização está limitada a estruturas simples para as quais soluções analíticas por ondas existam. A motivação por trás das formulações de matrizes de superelementos a partir do método dos elementos finitos ondulatórios está na utilização do conceito de ondas numéricas para calcular a resposta harmônica de sistemas mecânicos acoplados que envolvam estruturas com periodicidade unidimensional e junções elásticas a partir de procedimentos de montagem clássicos de elementos finitos ou técnicas de decomposição de domínio. Este assunto é tratado na terceira parte desta tese. Nesse caso, o método de Craig-Bampton é usado para expressar as matrizes de superelementos de junções por meio de modos estáticos e de interface fixa. Um critério baseado no método dos elementos finitos ondulatórios é considerado para a seleção dos modos da junção que mais contribuem para a resposta forçada do sistema. Isto também contribui para o aumento da eficiência da simulação numérica de sistemas acoplados. Finalmente, na quarta parte desta tese, o método dos elementos finitos ondulatórios é utilizado para mostrar que é possível projetar estruturas periódicas com potencial para funcionar como filtros de vibração em bandas de frequência específicas. Com o intuito de destacar a relevância dos desenvolvimentos propostos nessa tese, ensaios numéricos envolvendo guias de onda sólidos, pórticos planos e estruturas tridimensionais do tipo fuselagem aeronáutica são realizadosAbstract: In this thesis, the wave finite element (WFE) method is used for assessing the harmonic forced response of mechanical systems that involve structures with one-dimensional periodicity, i.e., structures which are made up of several identical substructures along one direction. Such mechanical systems can be quite complex and are commonly encountered in engineering applications, e.g., aircraft fuselages. The first part of the thesis is concerned with the computation of wave modes traveling along these structures. A brief literature review is presented regarding the available formulations for the WFE eigenproblem, which need to be solved for expressing the wave modes, as well as a study of the numerical errors induced by these eigenproblems in the case of a solid waveguide. In the second part of the thesis, the WFE-based superelement modeling of periodic structures is proposed. In this context, the dynamic stiffness matrices and receptance matrices of periodic structures are expressed in terms of wave modes. Compared to the conventional FE-based dynamic stiffness and receptance matrices, the WFE-based matrices can be computed in a very fast way without loss of accuracy. In addition, an accurate strategy for WFE-based model order reduction is presented. It provides significant computational time savings for the forced response analysis of periodic structures compared to WFE-based superelement modeling, which makes use of the full wave basis. Indeed, it is shown that higher-order numerical spectral elements can be built by means of the WFE method. This is an alternative to the conventional spectral element method, which is limited to simple structures for which closed-form wave solutions exist. The motivation behind the formulation of WFE-based superelement matrices is the use of the concept of numerical wave modes to assess the forced response of coupled mechanical systems that involve structures with one-dimensional periodicity and coupling elastic junctions through classic finite element assembly procedures or domain decomposition techniques. This issue is addressed in the third part of this thesis. In this case, the Craig-Bampton method is used to express superelement matrices of coupling junctions by means of static and fixed-interface modes. A WFE-based criterion is considered to select among junction modes those that contribute most to the system forced response. This also contributes to enhancing the efficiency of the numerical simulation of coupled systems. Finally, in the fourth part of this thesis, the WFE method is used to show the potential of designing periodic structures which work as vibration filters within specific frequency bands. In order to highlight the relevance of the developments proposed in this thesis, numerical experiments which involve solid waveguides, two-dimensional frame structures, and three-dimensional aircraft fuselage-like structures are carried outDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutora em Engenharia Mecânica2010/17317-9FAPES

FEATURE-BASED GEOMETRIC MODELLING AND ANALYSIS OF MULTIBODY MECHANICAL SYSTEM BEHAVIOUR

The aim of this paper is to present a modelling system and an application to analyse the mechanical behaviour of a gear-box. Designing a new type of gear-box, there is a real need for the concurrent engineering activities of the designers of geometric modelling, mesh generation and mechanical analysis. In this system own developed contact types of finite elements (FEM) have been used. The new system contains some programs of the earlier system ASSYM (CASM Lab.) for modelling the casing as the superstructure of a gear-box and its bearings as FEM contact-macroelements. In the proposed system the designers can use the modeller CAEDS (IBM Corp.) for feature-based geometric modelling and for generating the global mesh model of casing, the FEM analysis processor Mac/NASTRAN (MacNeal-Schwendler Corp.) and the new version of the N_SIM program (CASM Lab.) for modelling the pairs of gears and the bearings, furthermore the New Grid (N.G.) preprocessor (CASM Lab.). The N.G. can introduce the local mesh models of macroelements to the global mesh of gear-box casing

Acoustic finite element analysis of duct boundaries

The finite element method has been found to be useful for problems in acoustics. The method as presently applied is not efficient for several common acoustic geometries. This dissertation investigates problems associated with applying the finite element method to acoustic geometries with repeated or standard features and to geometries involving open boundary segments;Substructuring methods are modified and applied to problems involving internal acoustic propagation. It is found that substructuring can be usefully applied for transient response analysis, for frequency response analysis, for repeated geometries, and for parametric studies. Sub-structuring techniques are shown to be an inefficient substitute for higher order elements;Present techniques of modeling open boundary segments are reviewed. A new element shape function which includes both radiant and polynomial terms is developed. The element, termed the radiation element, is shown to be superior to other methods for modeling open boundary segments. The element is also shown to be superior to quadratic elements for modeling axisymmetric internal geometries. The FORTRAN code of a finite element computer program for acoustic applications is included in the Appendix. The program is capable of two-dimensional and axisymmetric superelement generation, potential flow analysis, eigenvalue analysis, and frequency response analysis

Development of simplified models for crashworthiness analysis.

Simplified modeling generates a great deal of interest in the area of crashworthiness analysis. Modeling methods used to create simplified computer models for crashworthiness have been well developed. In advanced simplified models, researchers develop simplified elements that can correctly predict structure\u27s crash behavior based on the existing collapse theories. These developed simplified elements then are applied to develop the simplified models. Nevertheless, most of the exiting collapse theories are regarding the thin-walled box section beams. However, in addition to the box section member, the channel section member is another popular member and is widely used in engineering for architectural structures, vehicles, and etc. Therefore, to simplify the thin-walled channel section beams, new collapse theory is required to predict the crash behavior for such beams. This topic is the focus of this dissertation. This dissertation develops a mathematical model to predict the crash behavior of the thin-walled channel section beams based on their real collapse mechanisms. The derived math formulae are verified through several basic applications. After that, both the existing collapse theories and the developed collapse theory regarding the thin-walled channel section beams are applied to simplify the detailed truck chassis model. The developed simplified model is used for crashworthiness analysis and the results are compared to those from the detailed model. The developed theory and the modeling method are then validated through the comparison. Additionally, in developing the simplified truck chassis model, the cross members that were modeled using coarse shell elements in previous simplified models are remodeled using simple elements. Two of the simplified modeling methods, the superelement method and the equivalent beam method, are utilized to generate the simplified models for the cross members of the truck chassis model. The principle of both methods is to use simple elements to transfer the original members\u27 mass and stiffness matrices. The equivalent beam method is recommended after comparison of the results of the crashworthiness analyses of each method. The primary contributions of this work are first, the derivation of crash theory that can predict the crash behavior of thin-walled channel section beams. The second is the use of equivalent beams to simplify the cross members within truck chassis models. Finally, a simplified modeling methodology is presented and evaluated. All the theory and modeling method developed in this work are applied for creating simplified models. Both the simplified and detailed models are used for crashworthiness analyses, results show that the errors caused by the simplified models are fewer than 10% and the simplified models only take less than 10% of the computer time of the corresponding detailed models

Sixth NASTRAN (R) Users' Colloquium

Papers are presented on NASTRAN programming, and substructuring methods, as well as on fluids and thermal applications. Specific applications and capabilities of NASTRAN were also delineated along with general auxiliary programs

A Finite Element Procedure for Calculating Fluid-Structure Interaction Using MSC/NASTRAN

This report is intended to serve two purposes. The first is to present a survey of the theoretical background of the dynamic interaction between a non-viscid, compressible fluid and an elastic structure is presented. Section one presents a short survey of the application of the finite element method (FEM) to the area of fluid-structure-interaction (FSI). Section two describes the mathematical foundation of the structure and fluid with special emphasis on the fluid. The main steps in establishing the finite element (FE) equations for the fluid structure coupling are discussed in section three. The second purpose is to demonstrate the application of MSC/NASTRAN to the solution of FSI problems. Some specific topics, such as fluid structure analogy, acoustic absorption, and acoustic contribution analysis are described in section four. Section five deals with the organization of the acoustic procedure flowchart. Section six includes the most important information that a user needs for applying the acoustic procedure to practical FSI problems. Beginning with some rules concerning the FE modeling of the coupled system, the NASTRAN USER DECKs for the different steps are described. The goal of section seven is to demonstrate the use of the acoustic procedure with some examples. This demonstration includes an analytic verification of selected FE results. The analytical description considers only some aspects of FSI and is not intended to be mathematically complete. Finally, section 8 presents an application of the acoustic procedure to vehicle interior acoustic analysis with selected results

Coupled approach to modelling damage in bonded composite structures

A fully coupled global-local approach for structural analysis has been developed. It is motivated by the need to use a range of scales and modelling techniques when designing a structure in composite materials. These range from the microscale at which the interfaces between fibres and matrix, or buckling of fibres themselves may play a role in the material behaviour, through intermediate scales where delamination and debonding may have an influence up to the macroscale where entire structures may be modelled with service loads directly applied. The method is based on passing boundary conditions from larger to smaller length scale models while passing information about damage and stiffness degradation up through the scales. By using nested levels of submodel, a greater range of length scales may be included in a single set of coupled analyses. Here an explanation of the methods of coupling two scales of solid models as well as coarse shell models to relatively refined solid models is presented. Each of these methods is validated against equivalent models using established modelling techniques, and are shown to produce results comparable to a complete model at the refined scale and preferable to other global-local approaches. Experimental tests have also been carried out on a stiffened panel with two stiffener runouts undergoing debonding. Not only did the coupling method model these tests accurately, but it was also shown to be more appropriate than simple submodelling in this case. A further demonstration of the techniques is included. The largest scale consisting of a shell element mesh is coupled with an intermediate scale with a continuum shell mesh, which in turn is coupled to a refined scale solid model. This demonstration shows how the methods developed here could be used to unify various analyses in the composites design process which until now have remained separate.Open Acces

Integrated durability analysis of a vehicle through virtual simulation.

The intent of this research is to create a high fidelity multibody dynamics model of a compact Sport Utility Vehicle (SUV) using CATIA, ADAMS and NASTRAN software suites. These software packages together are used to conduct virtual proving ground simulations. An MTS 329 series Road Test Simulator (RTS), which uses servo-hydraulic actuators to replicate vehicle proving ground is used to correlate results. The overall objective is to be able to predict component failure earlier in the design process, and to reduce the amount of time spent conducting physical durability tests. This thesis builds on research currently being conducted by many auto manufacturers in the area of virtual road test simulation. The development of a complete durability model is very complex, and involves many steps in simulating physical phenomena. This research focuses primarily on model creation techniques that are used to build a virtual multibody dynamics model, with an emphasis being placed on the construction, implementation and background theory of flexible bodies. (Abstract shortened by UMI.)Dept. of Mechanical, Automotive, and Materials Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .W66. Source: Masters Abstracts International, Volume: 44-01, page: 0428. Thesis (M.A.Sc.)--University of Windsor (Canada), 2003