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Two-dimensional Examples (two-dimensional + example)
Selected AbstractsCrystal topologies , the achievable and inevitable symmetriesACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2009Georg Thimm The link between the crystal topology and symmetry is examined, focusing on the conditions under which a structure with a given topology can exhibit a certain symmetry. By defining embeddings for quotient graphs (finite representations of crystal topologies) and the corresponding nets (the graph-theoretical equivalents of structures), a strong relationship between the automorphisms of the quotient graphs and the symmetry of the embedded net is established. This allows one to constrain the relative node positions under the premise that an embedding of a net has a certain symmetry, and allows one to assign nodes to equivalents of Wyckoff positions. Two-dimensional examples as well as known crystal structures are used to illustrate the findings. A comparison with a related publication and a discussion on whether constraints on distances between atoms and on bond angles result in restrictions on symmetry without causing confusion conclude the work. [source] A study of thickness optimization of golf club heads to maximize release velocity of ballsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2004Kenji Nakai Abstract In the present study, the shape optimization of a golf club head is investigated. The problem of maximizing the release velocity of the ball after impact is treated under the constraint of a specified weight of club head. The thickness distribution of the clubface is chosen as the design variable for optimization. The basis vector method, which is an approximating method for optimization problems in which the sensitivity cannot be derived analytically, is employed. The basis vector represents a fundamental change of shape, and it is preferable to obtaining effective results that the basis vectors be mutually independent. A simple approach to create the basis vectors using eigenmodes is also presented. The theory of impedance matching is confirmed numerically by a two-dimensional example. A three-dimensional example is given to show that this approach is effective for optimal design of the golf club head. Copyright © 2004 John Wiley & Sons, Ltd. [source] The fast Gauss transform for non-local integral FE modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2006E. Benvenuti Abstract Originally developed for fast solving multi-particle problems, the fast Gauss transform (FGT) is here applied to non-local finite element models of integral type (FEFGT). The focus is on problems requiring fine geometry discretization, as in the case of solutions that exhibit high gradients or boundary layers. As shown by one- and two-dimensional examples, the FEFGT algorithm combines the robustness of the finite element method with the outstanding computational efficiency of the FGT. Copyright © 2005 John Wiley & Sons, Ltd. [source] A continuum-to-atomistic bridging domain method for composite latticesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Mei Xu Abstract The bridging domain method is an overlapping domain decomposition approach for coupling finite element continuum models and molecular mechanics models. In this method, the total energy is decomposed into atomistic and continuum parts by complementary weight functions applied to each part of the energy in the coupling domain. To enforce compatibility, the motions of the coupled atoms are constrained by the continuum displacement field using Lagrange multipliers. For composite lattices, this approach is suboptimal because the internal modes of the lattice are suppressed by the homogeneous continuum displacement field in the coupling region. To overcome this difficulty, we present a relaxed bridging domain method. In this method, the atom set is divided into primary and secondary atoms; the relative motions between them are often called the internal modes. Only the primary atoms are constrained in the coupling region, which succeed in allowing these internal modes to fully relax. Several one- and two-dimensional examples are presented, which demonstrate improved accuracy over the standard bridging domain method. Copyright © 2009 John Wiley & Sons, Ltd. [source] Quasi-dual reciprocity boundary-element method for incompressible flow: Application to the diffusive,advective equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003C. F. Loeffler Abstract This work presents a new boundary-element method formulation called quasi-dual reciprocity formulation for heat transfer problems, considering diffusive and advective terms. The present approach has some characteristics similar to those of the so-called dual-reciprocity formulation; however, the mathematical developments of the quasi-dual reciprocity approach reduces approximation errors due to global domain interpolation. Some one- and two-dimensional examples are presented, the results being compared against those obtained from analytical and dual-reciprocity formulations. The method convergence is evaluated through analyses where the mesh is successively refined for various Peclet numbers, in order to assess the effect of the advective term. Copyright © 2003 John Wiley & Sons, Ltd. [source] A time-stepping method for stiff multibody dynamics with contact and friction,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2002Mihai Anitescu Abstract We define a time-stepping procedure to integrate the equations of motion of stiff multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complementarity equations. Stiffness is accommodated by a technique motivated by a linearly implicit Euler method. We show that the main subproblem, a linear complementarity problem, is consistent for a sufficiently small time step h. In addition, we prove that for the most common type of stiff forces encountered in rigid body dynamics, where a damping or elastic force is applied between two points of the system, the method is well defined for any time step h. We show that the method is stable in the stiff limit, unconditionally with respect to the damping parameters, near the equilibrium points of the springs. The integration step approaches, in the stiff limit, the integration step for a system where the stiff forces have been replaced by corresponding joint constraints. Simulations for one- and two-dimensional examples demonstrate the stable behaviour of the method. Published in 2002 by John Wiley & Sons, Ltd. [source] Stability and accuracy of a semi-implicit Godunov scheme for mass transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Scott F. Bradford Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||