Thesis submitted in fulfilment of the requirements for the degree Magister Technologiae: Mechanical Engineering in the Faculty of Engineering at the CAPE PENINSULA UNIVERSITY OF TECHNOLOGY, 2009 / Finite element analysis modelling of sheet metal stamping is an important step in the design of tooling and process parameters. One of the critical measurements to determine the effectiveness of a numerical model is its capability of accurately predicting failure modes. To be able to make accurate predictions of deformation, tool force, blank design, etc computer simulation is almost necessary. In the automotive industry the tooling design can now be made by computer and analysed with FEA, and the amount of prototypes required for qualifying a design before manufacturing commences is greatly reduced. Tool design is a specialized phase of tool engineering. While there are many diecutting operation, some of which are very complex, they can all be reduce to plain blanking , piercing, lancing, cutting off and parting, notching, shaving and trimming. The cutting action that occurs in the piercing is quite similar to that of the chip formation ahead of a cutting tool. The punch contact the material supported by the die and a pressure builds up occurs, When the elastic limit of the work material is the exceeded the material begins to flow plastically (plastic deformation). It is often impractical to pierce holes while forming, or before forming because they would become distorted in the forming operation. The aim of the research is to develop techniques that would reduce the amount time spent during the tool qualifying stage. By accurately setting a finite element simulation that closely matches the experimental or real-life situation we can great understand the material behaviour and properties before tool designing phase commences. In this analysis, during the piercing process of the drainage hole for a shock absorber seat, there is visible material tearing (on the neck) which as a result the component is rejected. This results in material wastage, and prolonged cycle time since the operation has to be now done separately at a different workstation.

Ce travail porte sur le développement d’une nouvelle méthode numérique intitulée « Meshless local Petrov Galerkin (MLPG) combinée à la méthode des volumes finis (MVF) » appliquée au calcul de structures. Elle est basée sur la résolution de la forme faible des équations aux dérivées partielles par une méthode de Petrov Galerkin comme en éléments finis, mais par contre l’approximation du champ de déplacement introduite dans la forme faible ne nécessite pas de maillage. Seul un ensemble de nœuds est réparti dans le domaine et l’approximation du champ de déplacement en un point ne dépend que de la distance de ce point par rapport aux nœuds qui l’entourent et non de l’appartenance à un certain élément fini. Les déformations et les déplacements sont déterminés aux différents nœuds par interpolation locale en utilisant les moindres carrés mobiles (MLS). Les valeurs des déformations aux nœuds sont exprimées en termes de valeurs nodales interpolées indépendamment des déplacements, en imposant simplement la relation déformation déplacement directement par collocation aux points nodaux. La procédure de calcul pour cette méthode est implémentée dans un programme de calcul développé sous MATLAB. Le code obtenu a été validé sur un certain nombre de cas tests par comparaison avec des solutions analytiques de référence et des calculs éléments finis comme ABAQUS. L’ensemble de ces tests a montré un bon comportement de la méthode (environs 0.0001% d’erreurs par rapport à la solution exacte). L’approche est étendue pour l’étude des poutres minces et pour l’analyse dynamique et stabilité. / This work concerns the development of a new numerical method entitled “Meshless Local Petrov- Galerkin (MLPG) combined with the Finite Volumes Method (FVM)” applied to the structural analysis. It is based on the resolution of the weak form of the partial differential equations by a method of Petrov Galerkin as in finite elements, but the approximation of the field of displacement introduced into the weak form does not require grid. The displacements and strains are given with the various nodes by local interpolation by using moving least squares (MLS). The values of the nodal strains are expressed in terms of interpolated nodal values independently of displacements, by simply imposing the strain displacement relationship directly by collocation at the nodal points. The procedure of calculation for this method is implemented in a computer code developed in MATLAB. The developed code was validated on a certain number of test cases by comparison with analytical solutions and finite elements results like ABAQUS. The whole of these tests showed a good behaviour of the method (about 0.0001% of errors in compared to the exact solution). The approach is also extended for the study of the thin beams and the dynamic analysis and stability.

Dans cette thèse, nous proposons de développer un outil de conception pour la mise en forme des bouteilles en PET par le procédé d'étirage-soufflage. Nous avons implémenté un logiciel de simulation numérique qui utilise une méthode meshless : la méthode des éléments naturels contraints (C-NEM). Pour alimenter le logiciel nous avons modélisé le comportement mécanique du PET par un modèle non linaire anisotrope. Pour modéliser le comportement du PET nous avons réalisé une série d’essais qui nous a permis de lier les propriétés macroscopiques à l'état de la microstructure Une fois la simulation d'étirage-soufflage effectuée, nous connaissons la géométrie de la bouteille ainsi que la description de sa microstructure : orientation et cristallinité. A partir du calcul précédent nous pouvons, à l'aide de la micromécanique linéaire, calculer la résistance de la bouteille finie à diverses sollicitations / In this thesis, we propose to develop a tool to design the stretch blow-molding process of PET bottles. We have implemented a software of numerical simulation which uses a meshless method : the constrained natural element method (C-NEM). In order to provide this software, we modeled the mechanical behaviour of PET by a non linaire anisotropic model. To model the behavior of PET we carried out a series of tests that allowed us to link the macroscopic properties to the state of the microstructure. Once the simulation of the stretch blow made, we know the geometry of the bottle and the description of its microstructure : orientation and crystallinity. From the previous calculation we can, using linear micromechanic, calculate the resistance of the bottle over to various loads

Dans cette thèse, nous proposons de développer un outil de conception pour la mise en forme des bouteilles en PET par le procédé d'étirage-soufflage. Nous avons implémenté un logiciel de simulation numérique qui utilise une méthode meshless : la méthode des éléments naturels contraints (C-NEM). Pour alimenter le logiciel nous avons modélisé le comportement mécanique du PET par un modèle non linaire anisotrope. Pour modéliser le comportement du PET nous avons réalisé une série d'essais qui nous a permis de lier les propriétés macroscopiques à l'état de la microstructure Une fois la simulation d'étirage-soufflage effectuée, nous connaissons la géométrie de la bouteille ainsi que la description de sa microstructure : orientation et cristallinité. A partir du calcul précédent nous pouvons, à l'aide de la micromécanique linéaire, calculer la résistance de la bouteille finie à diverses sollicitations

We investigate (i) pull-in instabilities in a microelectromechanical (MEM) beam due to the Coulomb force and in MEM membranes due to the Coulomb and the Casimir forces, and (ii) thermomechanical instability in a heat-conducting thermoelastoviscoplastic solid due to thermal softening overcoming hardening caused by strain- and strain-rate effects. Each of these nonlinear multiphysics problems is analyzed by the meshless local Petrov-Galerkin (MLPG) method. The moving least squares (MLS) approximation is used to generate basis functions for the trial solution, and the basis for test functions is taken to be either the weight functions used in the MLS approximation, or the same as for the trial solution. In this case the method becomes Bubnov-Galerkin. Essential (displacement, temperature, electric potential) boundary conditions are enforced by the method of Lagrange multipliers. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with either the displacement iteration pull-in extraction algorithm or the pseudoarclength continuation method. For the thermomechanical problem, the localization of deformation into narrow regions of intense plastic deformation is delineated. For every problem studied, computed results are found to compare well with those obtained either analytically or by the finite element (FE) method. For the same accuracy, the MLPG method generally requires fewer nodes but more CPU time than the FE method; thus additional computational cost is compensated somewhat by the increased efficiency of the MLPG method. / Ph. D.

The new approach of volume data visualization is presented in this paper. The proposed algorithm is based on point-based volume visualization. The main idea of it is to approximate volumetric dataset with surface made from points rather than approximate it with polygon-based iso-surface. This work covers a survey of volumetric data types, main principles of volume visualization and areas where improvements on algorithms of volume visualization are likely to be done. There is analysis of meshless iso-surface generation from multiblock data algorithm presented, suggesting dynamic iso-surface generation modification and some experiments based on these suggestions.

There is strong interest in the use of small low-cost highly sensitive magnetic field sensors for applications (such as small memory and biomedical devices) requiring weak field measurements. Among weak-field sensors, the magneto-impedance (MI) sensor has demonstrated an absolute resolution on the order of 10-11 T. The MI effect is a sensitive realignment of a periodic magnetization in response to an external magnetic field within small ferromagnetic structures. However, design of MI sensors has relied primarily on trial and error experimental methods along with decoupled models that separate the micromagnetic and classical electromagnetic equations describing the MI effect. To offer a basis for more cost-effective designs, this thesis research presentation begins with a general formulation describing MI sensors, which relaxes assumptions commonly made leading to decoupling. The coupled set of nonlinear equations is solved numerically using an efficient meshless method in a point collocation formulation. For the problem considered, the chosen method is shown to offer advantages over alternative methods including the finite element method. In the case of time, projection methods are used to stabilize the time discretization algorithm while quasi-Newton methods (nonlinear solver) are shown to be more computationally efficient, as well. Specifically, solutions for two MI sensor element geometries are presented, which were validated against published experimental data. While the examples illustrated here are for MI sensors, the approach presented can also be extended to other weak-field sensors like fluxgate and Hall effect sensors.

[Abstract]This thesis reports the development of new meshless schemes for solving timedependent partial differential equations (PDEs) and for the numerical simulation of some typical unsteady incompressible viscous flows.The new numerical schemes are based on the Idirect/Integrated Radial Basis Function Network (IRBFN) method which is fully meshless as no element-typemesh is required. The IRBFN method has been successfully applied to solve time-independent elliptic PDEs, some steady fluid flows and recently unsteady Navier-Stokes equations in streamfunction-vorticiy formulation using simple time integration methods (e.g. first-order backward Euler method). The main objective of the present research is to devise and implement meshless numerical schemes for unsteady problems in computational fluid dynamics where notonly the accuracy but also the efficiency and stability of the numerical schemes are of primary concerns. In addition, the effects of different parameters of theIRBFN method on the accuracy, stability and efficiency of the proposed numerical schemes are extensively studied in this research.As the first step in extending the IRBFN method to various types of timedependent PDEs, two numerical schemes combining the IRBFN method with high-order time stepping algorithms are developed for solving parabolic, hyperbolic,and advection-diffusion equations. Sensitivity analysis of the method to point density, time-step size and shape parameter are extensively performed to study the influence of these parameters to the overall accuracy of the method.A further extension of the IRBFN method for incompressible fluid flows with moving interfaces, especially for passive transport problems is accomplished in this research with a novel meshless approach in which the level set methodis coupled with the the IRBFN method for capturing moving interfaces in an ambient fluid flow without any explicit computation of the actual front location.Another contribution of this research is the development of two new meshless schemes based on the IRBFN method for the numerical simulation of unsteady incompressible viscous flows governed by the Navier-Stokes equations. In the new schemes, the splitting approach is used to deal with the momentum equation and the incompressibility constraint in a segregated manner. Numerical experiments on the new schemes in terms of accuracy and stability are performed for verification purposes.Finally, a novel meshless hybrid scheme is developed in this research to numerically simulate interfacial flows in which the motion and deformation of the interface between the two immiscible fluids are fully captured. Unlike the passive transport problems mentioned above where the influence of the moving interface on the surrounding fluid is ignored, the interfacial flows are studied here with the surface tension taken into account. As a result, a two-way interaction between the moving interface and the ambient flow is fully investigated.All numerical schemes developed in this research are verified through a wide range of transient problems including different kinds of time-dependent PDEs,typical passive transport problems and interfacial flows as well as unsteady incompressible viscous flows governed by Navier-Stokes equations.

Peridynamics (PD), a reformulation of the Classical Continuum Mechanics (CCM), is a new and promising meshless and nonlocal computational method in solid mechanics. To permit discontinuities, the PD integro-differential equation contains spatial integrals and time derivatives. PD can be considered as the continuum version of molecular dynamics. This feature of PD makes it a good candidate for multi-scale analysis of materials. Concurrently, the topology optimization has also been rapidly growing in view of the need to design lightweight and high performance structures. Therefore, this thesis presents the potential for a peridynamics-based topology optimization approach. To avoid the gradient calculations, a heuristic topology optimization method is employed. The minimization of the PD strain energy density is set as the objective function. The structure is optimized based on a modified solid isotropic material with a penalization approach and a projection scheme is utilized to obtain distinct results. Several test cases have been studied to analyze the suitability of the proposed method in topology optimization. / Graduate

Smoothed Particle Hydrodynamics (SPH) is a meshless numerical method which has long been put into practice for scientific and engineering applications. It arises as a numerical discretization of convolution-like integral operators that approximate local differential operators. There have been many studies on the SPH with an emphasis on its role as a numerical scheme for partial differential equations while little attention is paid to the underlying continuum nonlocal models that lie intermediate between the two. The main goal of this thesis is to provide mathematical understanding of the SPH-like meshless methods by means of ongoing developments in studies of nonlocal models with a finite range of nonlocal interactions. It is timely for such a work to be initiated with growing interests in the nonlocal models. The thesis touches on numerical, theoretical and modeling aspects of the nonlocal integro-differential equations pertaining to the SPH-like schemes. As illustrative examples of each aspect it presents robust SPH-like schemes for advection-convection equations, discusses the stabilities of nonsymmetric nonlocal gradient operators, and proposes a new formulation of nonlocal Dirichlet-like type boundary conditions.