Home About us Contact
|
Home About us Contact | ||
|
|
||
Essential Boundary Conditions (essential + boundary_condition)
Selected AbstractsMeshfree point collocation method for elasticity and crack problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Sang-Ho Lee Abstract A generalized diffuse derivative approximation is combined with a point collocation scheme for solid mechanics problems. The derivatives are obtained from a local approximation so their evaluation is computationally very efficient. This meshfree point collocation method has other advantages: it does not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. The accuracy of the solutions is exceptional and generally exceeds that of element-free Galerkin method with linear basis. The performance and robustness are demonstrated by several numerical examples, including crack problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Certified solutions for hydraulic structures using the node-based smoothed point interpolation method (NS-PIM)INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010J. Cheng Abstract A meshfree node-based smoothed point interpolation method (NS-PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node-based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS-PIM and the simulation results of NS-PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS-PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright © 2009 John Wiley & Sons, Ltd. [source] Modelling of contaminant transport through landfill liners using EFGMINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010R. Praveen Kumar Abstract Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection-dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element-free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd. [source] Some numerical issues using element-free Galerkin mesh-less method for coupled hydro-mechanical problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2009Mohammad Norouz Oliaei Abstract A new formulation of the element-free Galerkin (EFG) method is developed for solving coupled hydro-mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro-mechanical problems. Examples are studied and compared with closed-form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro-mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Imposition of essential boundary conditions by displacement constraint equations in meshless methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Xiong Zhang Abstract One of major difficulties in the implementation of meshless methods is the imposition of essential boundary conditions as the approximations do not pass through the nodal parameter values. As a consequence, the imposition of essential boundary conditions in meshless methods is quite awkward. In this paper, a displacement constraint equations method (DCEM) is proposed for the imposition of the essential boundary conditions, in which the essential boundary conditions is treated as a constraint to the discrete equations obtained from the Galerkin methods. Instead of using the methods of Lagrange multipliers and the penalty method, a procedure is proposed in which unknowns are partitioned into two subvectors, one consisting of unknowns on boundary ,u, and one consisting of the remaining unknowns. A simplified displacement constraint equations method (SDCEM) is also proposed, which results in a efficient scheme with sufficient accuracy for the imposition of the essential boundary conditions in meshless methods. The present method results in a symmetric, positive and banded stiffness matrix. Numerical results show that the accuracy of the present method is higher than that of the modified variational principles. The present method is a exact method for imposing essential boundary conditions in meshless methods, and can be used in Galerkin-based meshless method, such as element-free Galerkin methods, reproducing kernel particle method, meshless local Petrov,Galerkin method. Copyright © 2001 John Wiley & Sons, Ltd. [source] A natural neighbour Galerkin method with quadtree structureINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005J. J. Laguardia Abstract We describe in this paper a highly structured numerical method that allows for an important speedup in the calculations. The method is implemented in a bi-dimensional binary tree (quadtree or octree) structure in a partition of unity framework. The partition of unity is constructed by using natural neighbour interpolation. Data can be easily obtained from voxel or pixel-based images, as well as STL files or other CAD descriptions. The method described here possesses linear completeness at least and essential boundary conditions are implemented through the characteristic function method, by employing a special class of functions called R -functions. After the theoretical description of the method, some examples of its performance are presented and analysed. Copyright © 2005 John Wiley & Sons, Ltd. [source] On solving large strain hyperelastic problems with the natural element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005B. Calvo Abstract In this paper, an extension of the natural element method (NEM) is presented to solve finite deformation problems. Since NEM is a meshless method, its implementation does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results (extremely important in three-dimensional problems). NEM has important advantages over other meshless methods, such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The ,-NEM extension generalizes this behaviour to non-convex boundaries. A total Lagrangian formulation has been employed to solve different problems with large strains, considering hyperelastic behaviour. Several examples are presented in two and three dimensions, comparing the results with the ones of the finite element method. NEM performs better showing its important capabilities in this kind of applications. Copyright © 2004 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] Essential boundary condition enforcement in meshless methods: boundary flux collocation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Cheng-Kong C. Wu Abstract Element-free Galerkin (EFG) methods are based on a moving least-squares (MLS) approximation, which has the property that shape functions do not satisfy the Kronecker delta function at nodal locations, and for this reason imposition of essential boundary conditions is difficult. In this paper, the relationship between corrected collocation and Lagrange multiplier method is revealed, and a new strategy that is accurate and very simple for enforcement of essential boundary conditions is presented. The accuracy and implementation of this new technique is illustrated for one-dimensional elasticity and two-dimensional potential field problems. Copyright © 2001 John Wiley & Sons, Ltd. [source] On an implicit particle method for simulation of forming processesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005O. Schilling Task is the simulation of forming processes using particle methods. We implemented some mesh-free methods (the element free Galerkin method [1] and others) and the finite element method in one programme system which permits a direct comparison. For the mesh-free methods a moving least squares approximation is applied. The shape functions are not zero or one at the nodes, thus essential boundary conditions cannot be imposed directly [2]. We use a penalty method to enforce essential boundary conditions and contact conditions. The contact algorithm (normal contact of nodes to C1 -continuous surfaces) is checked by means of the element free Galerkin method and the FEM on the basis of numerical examples which deal with forming processes. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||