Dissertations / Theses on the topic 'Funte element method Data processing'

Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2009.<br>Committee Chair: Vuduc, Richard; Committee Member: Biros, George; Committee Member: Davatzikos, Christos; Committee Member: Tannenbaum, Allen; Committee Member: Zhou, Hao Min. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Studies of numerical methods to decouple structure and fluid interaction have reported the need for more precise approximations of higher structure eigenvalues and eigenvectors than are currently available from standard finite elements. The purpose of this study is to investigate hybrid finite element models composed of standard finite elements and exact-elements for the prediction of higher structure eigenvalues and eigenvectors. An exact beam-element dynamic-stiffness formulation is presented for a plane Timoshenko beam with rotatory inertia. This formulation is based on a converted continuum transfer matrix and is incorporated into a typical finite element program for eigenvalue/vector problems. Hybrid models using the exact-beam element generate transcendental, nonlinear eigenvalue problems. An eigenvalue extraction technique for this problem is also implemented. Also presented is a post-processing capability to reconstruct the mode shape each of exact element at as many discrete locations along the element as desired. The resulting code has advantages over both the standard transfer matrix method and the standard finite element method. The advantage over the transfer matrix method is that complicated structures may be modeled with the converted continuum transfer matrix without having to use branching techniques. The advantage over the finite element method is that fewer degrees of freedom are necessary to obtain good approximations for the higher eigenvalues. The reduction is achieved because the incorporation of an exact-beam-element is tantamount to the dynamic condensation of an infinity of degrees of freedom. Numerical examples are used to illustrate the advantages of this method. First, the eigenvalues of a fixed-fixed beam are found with purely finite element models, purely exact-element models, and a closed-form solution. Comparisons show that purely exact-element models give, for all practical purposes, the same eigenvalues as a closed-form solution. Next, a Portal Arch and a Verdeel Truss structure are modeled with hybrid models, purely finite element, and purely exact-element models. The hybrid models do provide precise higher eigenvalues with fewer degrees of freedom than the purely finite element models. The purely exact-element models were the most economical for obtaining higher structure eigenvalues. The hybrid models were more costly than the purely exact-element models, but not as costly as the purely finite element models.<br>Ph. D.

The accurate finite element analysis of subregions of large structures is difficult to carry out because of uncertainties about how the rest of the structure influences the boundary conditions and loadings of the subregion model. This dissertation describes the theoretical development and computer implementation of a new approach to this problem of modeling subregions. This method, the specified boundary stiffness/force (SBSF) method, results in accurate displacement and stress solutions as the boundary loading and the interaction between the stiffness of the subregion and the rest of the structure are taken into account. This method is computationally efficient because each time that the subregion model is analyzed, only the equations involving the degrees of freedom within the subregion model are solved. Numerical examples are presented which compare this method to some of the existing methods for subregion analysis on the basis of both accuracy of results and computational efficiency. The SBSF method is shown to be more accurate than another approximate method, the specified boundary displacement (SBD) method and to require approximately the same number of computations for the solution. For one case, the average error in the results of the SBD method was +2.75% while for the SBSF method the average error was -0.3%. The comparisons between the SBSF method and the efficient and exact zooming methods demonstrate that the SBSF method is less accurate than these methods but is computationally more efficient. In one example, the error for the exact zooming method was -0.9% while for the SBSF method it was -3.7%. Computationally, the exact zooming method requires almost 185% more operations than the SBSF method. Similar results were obtained for the comparison of the efficient zooming method and the SBSF method. Another use of the SBSF method is in the analysis of design changes which are incorporated into the subregion model but not into the parent model. In one subregion model a circular hole was changed to an elliptical hole. The boundary forces and stiffnesses from the parent model with the circular hole were used in the analysis of the modified subregion model. The results of the analysis of the most refined mesh in this example had an error of only -0.52% when compared to the theoretical result for the modified geometry. The results of the research presented in this dissertation indicate that the SBSF method is better suited to the analysis of subregions than the other methods documented in the literature. The method is both accurate and computationally efficient as well as easy to use and implement. The SBSF method can also be extended to the accurate analysis of subregion models with design changes which are not incorporated into the parent model.<br>Ph. D.

A finite element program is developed to depict the behavior of a sheet pile interlock connection in an axial pull test. Two types of sheet piles, PS32 and PSX32, are considered. The thumb and finger in the interlock of a sheet pile will provide three contact points for connection with another sheet pile. The problem is highly nonlinear in nature which involves large deflections and rotations, elastic-plastic material response, and a nonlinear boundary effect due to multi-contact surfaces. The Updated Lagrangian formulation is adopted in this study. When the response is in elastic range the Updated Lagrangian with Transformation is used while the Updated Lagrangian with Jaumann stress rate is employed when the element starts to yield. An elastic-plastic with isotropic strain hardening material model is used. The yielding of an element is detected by the Von Mises yield criterion. The finite element formulation also includes a moving contact algorithm to incorporate with both geometric and material nonlinearities. Incremental potential of contact forces for a discretized system is constructed such that geometric compatibilities are maintained between contacting bodies. A method to calculate contact tractions from residual load of internal element stresses is employed. The incremental equilibrium equation is solved by a Newton-Raphson technique. Convergence criteria based on incremental displacement, incremental internal energy of the system, and the changes in contact forces can be chosen to advance or terminate the iteration process.<br>Ph. D.

A general review of lattice dome geometry and connection details, leads to a modeling approach, which introduces intermediate elements to represent connections. The method provides improved modeling of joint behavior and flexibility for comparative studies. The discussion of lattice domes is further specialized for parallel lamella geometry. A procedure is developed for minimizing the number of different member lengths. This procedure is incorporated into a program, which generates the geometric data for a specified dome. The model is developed from a background which considers commercial space frame systems, static and dynamic loads, and modeling techniques using ABAQUS, a finite element program. An optional output of the generation program creates input data for ABAQUS. Modal analysis, static design loads, and earthquake loads are used in the evaluation of the model.<br>Master of Science

In this thesis, frontal subroutines are implemented to a plane frame analysis program for execution on the IBM PC. The resulting program solves for the unknown joint displacements of frame structures with large numbers of degrees of freedom by utilizing a peripheral back-up storage; which can not be analyzed directly in core. A comparison of the frontal solver and the out-of-core band solver is presented.<br>M.S.

A direct solution procedure is proposed and developed which exploits the parallelism that exists in current symmetric multiprocessing (SMP) multi-core processors. Several algorithms are proposed and developed to improve the performance of the direct solution of FE problems. A high-performance sparse direct solver is developed which allows experimentation with the newly developed and existing algorithms. The performance of the algorithms is investigated using a large set of FE problems. Furthermore, operation count estimations are developed to further assess various algorithms. An out-of-core version of the solver is developed to reduce the memory requirements for the solution. I/O is performed asynchronously without blocking the thread that makes the I/O request. Asynchronous I/O allows overlapping factorization and triangular solution computations with I/O. The performance of the developed solver is demonstrated on a large number of test problems. A problem with nearly 10 million degree of freedoms is solved on a low price desktop computer using the out-of-core version of the direct solver. Furthermore, the developed solver usually outperforms a commonly used shared memory solver.

The increasingly competitive market is forcing the industry to develop higher-quality products more quickly and less expensively. Engineering analysis, at the same time, plays an important role in helping designers evaluate the performance of the designed product against design requirements. In the context of automated CAD/FEA integration, the domain-dependent engineers different usage views toward product models cause an information gap between CAD and FEA models, which impedes the interoperability among these engineering tools and the automatic transformation from an idealized design model into a solvable FEA model. Especially in highly coupled variable topology multi-body (HCVTMB) problems, this transformation process is usually very labor-intensive and time-consuming. In this dissertation, a knowledge-based FEA modeling method, which consists of three information models and the transformation processes between these models, is presented. An Analysis Building Block (ABB) model represents the idealized analytical concepts in a FEA modeling process. Solution Method Models (SMMs) represent these analytical concepts in a solution technique-specific format. When FEA is used as the solution technique, an SMM consists of a Ready to Mesh Model (RMM) and a Control Information Model (CIM). An RMM is obtained from an ABB through geometry manipulation so that the quality mesh can be automatically generated using FEA tools. CIMs contain information that controls the FEA modeling and solving activities. A Solution Tool Model (STM) represents an analytical model at the tool-specific level to guide the entire FEA modeling process. Two information transformation processes are presented between these information models. A solution method mapping transforms an ABB into an RMM through a complex cell decomposition process and an attribute association process. A solution tool mapping transforms an SMM into an STM by mimicking an engineers selection of FEA modeling operations. Four HCVTMB industrial FEA modeling cases are presented for demonstration and validation. These involve thermo-mechanical analysis scenarios: a simple chip package, a Plastic Ball Grid Array (PBGA), and an Enhanced Ball Grid Array (EBGA), as well as a thermal analysis scenario: another PBGA. Compared to traditional methods, results indicate that this method provides better knowledge capture and decreases the modeling time from days/hours to hours/minutes.

Este trabalho trata do desenvolvimento de um sistema computacional, para a geração de dados e apresentação de resultados, específico para as estruturas de edifícios. As rotinas desenvolvidas devem trabalhar em conjunto com um sistema computacional para análise de estruturas com base no Método dos Elementos Finitos, contemplando tanto as estruturas de pavimentos; com a utilização de elementos de barra, placa/casca e molas; como as estruturas de contraventamento; com a utilização de elementos de barra tridimensional e recursos especiais como nó mestre e trechos rígidos. A linguagem computacional adotada para a elaboração das rotinas mencionadas é o Object Pascal do DELPHI, um ambiente de programação visual estruturado na programação orientada a objetos do Object Pascal. Essa escolha tem como objetivo, conseguir um sistema computacional onde alterações e adições de funções possam ser realizadas com facilidade, sem que todo o conjunto de programas precise ser analisado e modificado. Por fim, o programa deve servir como um verdadeiro ambiente para análise de estruturas de edifícios, controlando através de uma interface amigável com o usuário uma série de outros programas já desenvolvidos em FORTRAN, como por exemplo o dimensionamento de vigas, pilares, etc.<br>This work deals with a pre and pos data processing computational system specific for building structures. This computational system has been developed to work together with a finite element program for structural analysis, and it must include elements for flood structures analysis, as bars, plates, membranes and springs; and elements for bracing structures, as 3D-bar and rigid elements. Borland\'s Delphi, a rapid application development environment based on Object Pascal, has been used in this work. The reason for this choice is to provide an easy way to future modifications and additions in the source code. Finally, the developed system should make possible the integration, through user friendly interfaces, with other programs already developed in Fortran, for instance, for designing beams, columns, and others structural elements.

Ma Mun Chung.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.<br>Includes bibliographical references (leaves 86-88).<br>Abstract also in Chinese.<br>Abstract --- p.i<br>Declaration --- p.ii<br>Acknowledgement --- p.iii<br>List of Figures --- p.iv<br>List of Tables --- p.ix<br>Table of Contents --- p.x<br>Chapter 1. --- Introduction --- p.1<br>Chapter 1.1. --- Motivation --- p.1<br>Chapter 1.2. --- Thesis Roadmap --- p.3<br>Chapter 1.3. --- Contribution<br>Chapter 2. --- System Architecture --- p.6<br>Chapter 2.1. --- Tracker system --- p.6<br>Chapter 2.1.1. --- Spatial Information --- p.6<br>Chapter 2.1.2. --- Transmitter (Xmtr) --- p.6<br>Chapter 2.1.3. --- Receiver (Recvr) --- p.7<br>Chapter 2.2. --- Glove System --- p.7<br>Chapter 2.2.1. --- CyberGlove Interface Unit (CGIU) --- p.7<br>Chapter 2.2.2. --- Bend Sensors --- p.7<br>Chapter 2.3. --- Integrating the tracker and the glove system --- p.9<br>Chapter 2.3.1. --- System Layout --- p.9<br>Chapter 3. --- Deformable Model --- p.11<br>Chapter 3.1. --- Elastic models in computer --- p.11<br>Chapter 3.2. --- Virtual object model --- p.17<br>Chapter 3.3. --- Force displacement relationship --- p.18<br>Chapter 3.3.1. --- Stress-strain relationship --- p.19<br>Chapter 3.3.2. --- Stiffness matrix formulation --- p.20<br>Chapter 3.4. --- Solving the linear system --- p.24<br>Chapter 3.5. --- Implementation --- p.26<br>Chapter 3.5.1. --- Data structure --- p.26<br>Chapter 3.5.2. --- Global stiffness matrix formulation --- p.27<br>Chapter 3.5.3. --- Re-assemble of nodal displacement --- p.30<br>Chapter 4. --- Collision Detection --- p.32<br>Chapter 4.1. --- Related Work --- p.31<br>Chapter 4.2. --- Spatial Subdivision --- p.37<br>Chapter 4.3. --- Hierarchy construction --- p.38<br>Chapter 4.3.1. --- Data structure --- p.39<br>Chapter 4.3.2. --- Initialisation --- p.41<br>Chapter 4.3.3. --- Expanding the hierarchy --- p.42<br>Chapter 4.4. --- Collision detection --- p.45<br>Chapter 4.4.1. --- Hand Approximation --- p.45<br>Chapter 4.4.2. --- Interference tests --- p.47<br>Chapter 4.4.3. --- Searching the hierarchy --- p.51<br>Chapter 4.4.4. --- Exact interference test --- p.51<br>Chapter 4.5. --- Grasping mode --- p.53<br>Chapter 4.5.1. --- Conditions for Finite Element Analysis (FEA) --- p.53<br>Chapter 4.5.2. --- Attaching conditions --- p.53<br>Chapter 4.5.3. --- Collision avoidance --- p.54<br>Chapter 4.6. --- Repeating deformation in different orientation --- p.56<br>Chapter 5. --- Enhancing performance --- p.59<br>Chapter 5.1. --- Data communication --- p.60<br>Chapter 5.1.1. --- Client-server model --- p.60<br>Chapter 5.1.2. --- Internet protocol suite --- p.61<br>Chapter 5.1.3. --- Berkeley socket --- p.61<br>Chapter 5.1.4. --- Checksum problem --- p.62<br>Chapter 5.2. --- Use of parallel tool --- p.62<br>Chapter 5.2.1. --- Parallel code generation --- p.63<br>Chapter 5.2.2. --- Optimising parallel code --- p.64<br>Chapter 6. --- Implementation and Results --- p.65<br>Chapter 6.1. --- Supporting functions --- p.65<br>Chapter 6.1.1. --- Read file --- p.66<br>Chapter 6.1.2. --- Keep shape --- p.67<br>Chapter 6.1.3. --- Save as --- p.67<br>Chapter 6.1.4. --- Exit --- p.67<br>Chapter 6.2. --- Visual results --- p.67<br>Chapter 6.3. --- An operation example --- p.75<br>Chapter 6.4. --- Performance of parallel algorithm --- p.78<br>Chapter 7. --- Conclusion and Future Work --- p.84<br>Chapter 7.1. --- Conclusion --- p.84<br>Chapter 7.2. --- Future Work --- p.84<br>Reference --- p.86<br>Appendix A Matrix Inversion --- p.89<br>Appendix B Derivation of Equation 6.1 --- p.92<br>Appendix C Derivation of (6.2) --- p.93

Indiana University-Purdue University Indianapolis (IUPUI)<br>Nanocomposite ceramics have been widely studied in order to tailor desired properties at high temperatures. Methodologies for development of material design are still under effect. While finite element modeling (FEM) provides significant insight on material behavior, few design researchers have addressed the design paradox that accompanies this rapid design space expansion. A surrogate optimization model management framework has been proposed to make this design process tractable. In the surrogate optimization material design tool, the analysis cost is reduced by performing simulations on the surrogate model instead of high fidelity finite element model. The methodology is incorporated to and the optimal number of silicon carbide (SiC) particles, in a silicon-nitride(Si3N4) composite with maximum fracture energy [2]. Along with a deterministic optimization algorithm, model uncertainties have also been considered with the use of robust design optimization (RDO) method ensuring a design of minimum sensitivity to changes in the parameters. These methodologies applied to nanocomposites design have a significant impact on cost and design cycle time reduced.

This thesis presents an investigation of the modelling and optimal design of a particular 3-degree-of-freedom (DOF) XYθz micro-motion stage. This stage provides micron-scale motion in X and Y directions and a rotation about the Z-axis. Such a stage can be used for applications where positioning of components with micrometre, or even nanometre positioning accuracy is required. Some applications are; the positioning of samples in a scanning-electron-microscope; the positioning of masks in lithography; aligning fibre-optics and lasers; and manipulation of micro-scale objects in micro-biology or micro-systems assembly. The XYθz micro-motion stage investigated in this study uses a particular topology of monolithic compliant mechanism and three stack piezoelectric actuators. The compliant mechanism used is a 3RRR (three revolute-revolute-revolute) parallel compliant mechanism using flexure hinges. This parallel mechanism uses three RRR linkages. Each of the three RRR linkages uses three circular profile flexure hinges. Each flexure hinge provides predominantly rotational motion about one axis. This topology of mechanism has a symmetrical structure and provides numerous advantages that make it appropriate for use in a micro-motion stage. However, as yet this topology of compliant mechanism has only been investigated by a handful of researchers and it has not been used in any commercially developed systems. The design methodology of a stage using the 3RRR compliant mechanism has not been investigated in detail. In this thesis a study is presented that investigates different approaches to model the 3RRR compliant mechanism and also considers the piezo-actuator modelling, to give the complete XYθz micro-motion stage. Three models are presented and compared; the Pseudo-Rigid-Body Model (PRBM); a two-dimensional Finite-Element-Model (2-D FEM); and a third model is developed that is similar to the PRBM, but uses analytical equations to model the multiple degree-of-freedom compliance of the flexure hinges. The models developed are then used in parametric study so that the relationship between design parameters and output behaviour can be understood. An optimal design approach is then presented to develop an XYθz micro-motion stage for a particular application in a Scanning-Electron-Microscope (SEM). Finally experimental validation of the models is presented. The results of this study indicate which modelling approaches are accurate enough to prove useful for design, while also considering which models are computationally simple enough to be efficient and easy to use. The kinematic and dynamic behaviour of the 3RRR compliant mechanism and XYθz micro-motion stage is discussed in detail. This includes; a comprehensive description of the stage workspace, defining reachable and constant-rotation workspace areas; a discussion of actuator coupling; and in depth investigation of the modes of vibration. The results of the parametric study provide useful insight to aid the design of the XYz micro-motion stage and help simplify optimal design. The parametric study also highlights the difference in trends predicted by different modelling methods, which demonstrates the importance of using an appropriate model in design. The experimental validation demonstrates the accuracy of some modelling approaches while highlighting the limited accuracy of others.<br>http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1272186<br>Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2007

This thesis presents an investigation of the modelling and optimal design of a particular 3-degree-of-freedom (DOF) XYθz micro-motion stage. This stage provides micron-scale motion in X and Y directions and a rotation about the Z-axis. Such a stage can be used for applications where positioning of components with micrometre, or even nanometre positioning accuracy is required. Some applications are; the positioning of samples in a scanning-electron-microscope; the positioning of masks in lithography; aligning fibre-optics and lasers; and manipulation of micro-scale objects in micro-biology or micro-systems assembly. The XYθz micro-motion stage investigated in this study uses a particular topology of monolithic compliant mechanism and three stack piezoelectric actuators. The compliant mechanism used is a 3RRR (three revolute-revolute-revolute) parallel compliant mechanism using flexure hinges. This parallel mechanism uses three RRR linkages. Each of the three RRR linkages uses three circular profile flexure hinges. Each flexure hinge provides predominantly rotational motion about one axis. This topology of mechanism has a symmetrical structure and provides numerous advantages that make it appropriate for use in a micro-motion stage. However, as yet this topology of compliant mechanism has only been investigated by a handful of researchers and it has not been used in any commercially developed systems. The design methodology of a stage using the 3RRR compliant mechanism has not been investigated in detail. In this thesis a study is presented that investigates different approaches to model the 3RRR compliant mechanism and also considers the piezo-actuator modelling, to give the complete XYθz micro-motion stage. Three models are presented and compared; the Pseudo-Rigid-Body Model (PRBM); a two-dimensional Finite-Element-Model (2-D FEM); and a third model is developed that is similar to the PRBM, but uses analytical equations to model the multiple degree-of-freedom compliance of the flexure hinges. The models developed are then used in parametric study so that the relationship between design parameters and output behaviour can be understood. An optimal design approach is then presented to develop an XYθz micro-motion stage for a particular application in a Scanning-Electron-Microscope (SEM). Finally experimental validation of the models is presented. The results of this study indicate which modelling approaches are accurate enough to prove useful for design, while also considering which models are computationally simple enough to be efficient and easy to use. The kinematic and dynamic behaviour of the 3RRR compliant mechanism and XYθz micro-motion stage is discussed in detail. This includes; a comprehensive description of the stage workspace, defining reachable and constant-rotation workspace areas; a discussion of actuator coupling; and in depth investigation of the modes of vibration. The results of the parametric study provide useful insight to aid the design of the XYz micro-motion stage and help simplify optimal design. The parametric study also highlights the difference in trends predicted by different modelling methods, which demonstrates the importance of using an appropriate model in design. The experimental validation demonstrates the accuracy of some modelling approaches while highlighting the limited accuracy of others.<br>Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2007