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High Convergence Rates (high + convergence_rate)
Selected AbstractsA simplified method for lateral response analysis of suspension bridges under wind loadsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2006Jin Cheng Abstract A simplified method for analysing lateral response of suspension bridges under wind loads is proposed in this paper. The geometric non-linearity in the deflection theory and the three components of displacement-dependent wind loads are taken into account in the method. The analytical formulas for calculating the torsional, vertical, and lateral responses of suspension bridges under wind loads are derived. An iterative procedure, which has a high convergence rate for solving the problem, is developed. The proposed method is sufficient and simple to use. Wind-induced lateral response analysis of a long-span suspension bridge demonstrates the proposed method's efficiency and accuracy. Copyright © 2006 John Wiley & Sons, Ltd. [source] Moving kriging interpolation and element-free Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Lei Gu Abstract A new formulation of the element-free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary conditions in the EFG method often presents difficulties because the Kronecker delta property, which is satisfied by finite element shape functions, does not necessarily hold for the EFG shape function. The proposed new formulation of EFG eliminates this shortcoming through the moving kriging (MK) interpolation. Two major properties of the MK interpolation: the Kronecker delta property (,I(sJ)=,IJ) and the consistency property (,In,I(x)=1 and ,In,I(x)xIi=xi) are proved. Some preliminary numerical results are given. Copyright © 2002 John Wiley & Sons, Ltd. [source] A Cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Phong B. H. Le Abstract In this paper, high-order systems are reformulated as first-order systems, which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretization with 1D-integrated radial basis function networks (1D-IRBFN) (Numer. Meth. Partial Differential Equations 2007; 23:1192,1210). The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN, which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well-known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates. Copyright © 2009 John Wiley & Sons, Ltd. [source] Meshless analysis of potential problems in three dimensions with the hybrid boundary node methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004Jianming Zhang Abstract Combining a modified functional with the moving least-squares (MLS) approximation, the hybrid boundary node method (Hybrid BNM) is a truly meshless, boundary-only method. The method may have advantages from the meshless local boundary integral equation (MLBIE) method and also the boundary node method (BNM). In fact, the Hybrid BNN requires only the discrete nodes located on the surface of the domain. The Hybrid BNM has been applied to solve 2D potential problems. In this paper, the Hybrid BNM is extended to solve potential problems in three dimensions. Formulations of the Hybrid BNM for 3D potential problems and the MLS approximation on a generic surface are developed. A general computer code of the Hybrid BNM is implemented in C++. The main drawback of the ,boundary layer effect' in the Hybrid BNM in the 2D case is circumvented by an adaptive face integration scheme. The parameters that influence the performance of this method are studied through three different geometries and known analytical fields. Numerical results for the solution of the 3D Laplace's equation show that high convergence rates with mesh refinement and high accuracy are achievable. Copyright © 2004 John Wiley & Sons, Ltd. [source] The p-version of the FEM for computational contact mechanicsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008David Franke Contact analyses are being performed in various engineering applications. Here, like in most other fields, FE codes are based on low order elements using linear or quadratic shape functions. The intention of this paper is to show that finite elements with shape functions of high polynomial degree (p -FEM) are a very attractive alternative to low order elements, even for computational contact mechanics. One of the advantages is the possibility to enhance the element formulation with the blending function method in order to accurately discretize the given geometry, which leads in combination with high convergence rates to very efficient computations. In order to solve the problem of frictionless contact, a penalty formulation is applied in this work. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||