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Selected AbstractsKinematic and dynamic analysis of open-loop mechanical systems using non-linear recursive formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2006Yunn-Lin Hwang Abstract In this paper, a non-linear recursive formulation is developed for kinematic and dynamic analysis of open-loop mechanical systems. The non-linear equations of motion are developed for deformable links that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial co-ordinates as well as the assumed displacement field, and these time invariant quantities represent the dynamic coupling between the rigid-body modes and elastic deformations. A new recursive formulation is presented for solving equations of motion for open-loop chains consisting of interconnected rigid and deformable open-loop mechanical systems. This formulation is expressed by the recursive relationships and the generalized non-linear equations for deformable mechanical systems to obtain a large system of loosely coupled equations of motion. The main processor program consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic co-ordinates. Simultaneously, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic co-ordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The solution techniques used in this investigation yield a much smaller operations count and can more efficiently implement in any computer. The algorithms and solutions presented in this paper are illustrated by using an industrial robotic manipulator system. The numerical results using this formulation are also presented and discussed in this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003S. L. Crouch Abstract This paper considers the problem of an infinite, isotropic elastic plane containing an arbitrary number of non-overlapping circular holes and isotropic elastic inclusions. The holes and inclusions are of arbitrary size and the elastic properties of all of the inclusions can, if desired, be different. The analysis is based on the two-dimensional version of Somigliana's formula, which gives the displacements at a point inside a region V in terms of integrals of the tractions and displacements over the boundary S of this region. We take V to be the infinite plane, and S to be an arbitrary number of circular holes within this plane. Any (or all) of the holes can contain an elastic inclusion, and we assume for simplicity that all inclusions are perfectly bonded to the material matrix. The displacements and tractions on each circular boundary are represented as truncated Fourier series, and all of the integrals involved in Somigliana's formula are evaluated analytically. An iterative solution algorithm is used to solve the resulting system of linear algebraic equations. Several examples are given to demonstrate the accuracy and efficiency of the numerical method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Face modeling and editing with statistical local feature control modelsINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 6 2007Yu Zhang Abstract This article presents a novel method based on statistical facial feature control models for generating realistic controllable face models. The local feature control models are constructed based on the exemplar 3D face scans. We use a three-step model fitting approach for the 3D registration problem. Once we have a common surface representation for examples, we form feature shape spaces by applying a principal component analysis (PCA) to the data sets of facial feature shapes. We compute a set of anthropometric measurements to parameterize the exemplar shapes of each facial feature in a measurement space. Using PCA coefficients as a compact shape representation, we approach the shape synthesis problem by forming scattered data interpolation functions that are devoted to the generation of desired shape by taking the anthropometric parameters as input. The correspondence among all exemplar face textures is obtained by parameterizing a 3D generic mesh over a 2D image domain. The new feature texture with desired attributes is synthesized by interpolating the exemplar textures. With the exception of an initial tuning of feature point positions and assignment of texture attribute values, our method is fully automated. In the resulting system, users are assisted in automatically generating or editing a face model by controlling the high-level parameters. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 341,358, 2007 [source] On a model for electromagnetic processes inside and outside a ferromagnetic bodyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2008Martin Brokate Abstract One-dimensional Maxwell's equations are considered in a ferromagnetic body surrounded by vacuum. Existence and uniqueness of solution for the resulting system of partial differential equations with hysteresis on the whole real line is proved under suitable constitutive hypotheses. Copyright © 2008 John Wiley & Sons, Ltd. [source] Amplitude,shape approximation as an extension of separation of variablesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2008N. Parumasur Abstract Separation of variables is a well-known technique for solving differential equations. However, it is seldom used in practical applications since it is impossible to carry out a separation of variables in most cases. In this paper, we propose the amplitude,shape approximation (ASA) which may be considered as an extension of the separation of variables method for ordinary differential equations. The main idea of the ASA is to write the solution as a product of an amplitude function and a shape function, both depending on time, and may be viewed as an incomplete separation of variables. In fact, it will be seen that such a separation exists naturally when the method of lines is used to solve certain classes of coupled partial differential equations. We derive new conditions which may be used to solve the shape equations directly and present a numerical algorithm for solving the resulting system of ordinary differential equations for the amplitude functions. Alternatively, we propose a numerical method, similar to the well-established exponential time differencing method, for solving the shape equations. We consider stability conditions for the specific case corresponding to the explicit Euler method. We also consider a generalization of the method for solving systems of coupled partial differential equations. Finally, we consider the simple reaction diffusion equation and a numerical example from chemical kinetics to demonstrate the effectiveness of the method. The ASA results in far superior numerical results when the relative errors are compared to the separation of variables method. Furthermore, the method leads to a reduction in CPU time as compared to using the Rosenbrock semi-implicit method for solving a stiff system of ordinary differential equations resulting from a method of lines solution of a coupled pair of partial differential equations. The present amplitude,shape method is a simplified version of previous ones due to the use of a linear approximation to the time dependence of the shape function. Copyright © 2007 John Wiley & Sons, Ltd. [source] Non-linear dynamic contact of thin-walled structuresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Thomas Cichosz In many areas of mechanical engineering contact problems of thin,walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment,rotation characteristics of a bolted beam,column joint, contact occurs. Effective simulation of these and other contact problems, especially in three,dimensional non,linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin,walled character and dynamic effects into account. We use a segment,to,segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized-, Method and the Generalized Energy,Momentum Method. Using the "Velocity,Update" Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Quadratic metric-affine gravityANNALEN DER PHYSIK, Issue 4 2005D. Vassiliev Abstract We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is (purely) quadratic in curvature and study the resulting system of Euler,Lagrange equations. In the first part of the paper we look for Riemannian solutions, i.e. solutions whose connection is Levi-Civita. We find two classes of Riemannian solutions: 1) Einstein spaces, and 2) spacetimes with pp-wave metric of parallel Ricci curvature. We prove that for a generic quadratic action these are the only Riemannian solutions. In the second part of the paper we look for non-Riemannian solutions. We define the notion of a "Weyl pseudoinstanton" (metric compatible spacetime whose curvature is purely of Weyl type) and prove that a Weyl pseudoinstanton is a solution of our field equations. Using the pseudoinstanton approach we construct explicitly a non-Riemannian solution which is a wave of torsion in a spacetime with Minkowski metric. We discuss the possibility of using this non-Riemannian solution as a mathematical model for the neutrino. [source] A finite volume,multigrid method for flow simulation on stratified porous media on curvilinear co-ordinate systemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2001Pablo Calvo Abstract This paper presents a numerical study of infiltration processes on stratified porous media. The study is carried out to examine the performance of a finite volume method on problems with discontinuous solutions due to the transmission conditions in the interfaces. To discretize the problem, a curvilinear co-ordinate system is used. This permits matching the interface with the boundary of the control volumes that interchange fluxes between layers. The use of the multigrid algorithm for the resulting systems of equations allows problems involving a large number of nodes with low computational cost to be solved. Finally, some numerical experiments, which show the capillary barrier behaviour depending on the material used for the different layers and the geometric design of the interface, are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Synthesis and physical properties of low-molecular-weight redistributed poly(2,6-dimethyl-1,4-phenylene oxide) for epoxy resinJOURNAL OF APPLIED POLYMER SCIENCE, Issue 3 2008Hann-Jang Hwang Abstract Low-molecular-weight poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) was prepared by the redistribution of regular PPO with 4,4,-isopropylidenediphenol (bisphenol A) with benzoyl peroxide as an initiator in toluene. The redistributed PPO was characterized by proton nuclear magnetic resonance, mass spectra, and Fourier transform infrared spectroscopy. The redistributed PPO oligomers with terminal phenolic hydroxyl groups and low molecular weights (weight-average molecular weight = 800,4000) were used in the modification of a diglycidyl ether of bisphenol A/4,4,-diaminodiphenylmethane network system. The curing behaviors were investigated by differential scanning calorimetry and Fourier transform infrared spectroscopy. The effect of molecular weight and the amount of redistributed PPO oligomers incorporated into the network on the physical properties of the resulting systems were investigated. The thermal properties of the cured redistributed PPO/epoxy resins were studied by dynamic mechanical analysis, thermal mechanical analysis, thermogravimetric analysis, and dielectric analysis. These cured redistributed PPO/epoxy resins exhibited lower dielectric constants, dissipation factors, coefficients of thermal expansion, and moisture absorptions than those of the control diglycidyl ether of bisphenol A based epoxy. The effects of the composition on the glass-transition temperature and thermal stability are discussed. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008 [source] Analysis of a block red-black preconditioner applied to the Hermite collocation discretization of a model parabolic equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2001Stephen H. Brill Abstract We are concerned with the numerical solution of a model parabolic partial differential equation (PDE) in two spatial dimensions, discretized by Hermite collocation. In order to efficiently solve the resulting systems of linear algebraic equations, we choose the Bi-CGSTAB method of van der Vorst (1992) with block Red-Black Gauss-Seidel (RBGS) preconditioner. In this article, we give analytic formulae for the eigenvalues that control the rate at which Bi-CGSTAB/RBGS converges. These formulae, which depend on the location of the collocation points, can be utilized to determine where the collocation points should be placed in order to make the Bi-CGSTAB/RBGS method converge as quickly as possible. Along these lines, we discuss issues of choice of time-step size in the context of rapid convergence. A complete stability analysis is also included. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:584,606, 2001 [source] |