Your search yielded the following manuscripts:

• J. S. Chen, C. T. Wu, S. Yoon, Nonlinear Version of Stabilized Conforming Nodal Integration for Galerkin Meshfree Methods
  Keywords: Nodal Integration, Stabilization Method, Meshfree Method, Moving Least-Square, Reproducing Kernel, Nonlinear Mechanics
  Abstract: A stabilized conforming (SC) nodal integration, which meets the integration constraint in the Galerkin meshfree approximation, is generalized for nonlinear problems. Using a Lagrangian discretization, the integration constraints for SC nodal integration are imposed in the undeformed configuration. This is accomplished by introducing a Lagrangian strain smoothing to the deformation gradient, and by performing a nodal integration in the undeformed configuration. The proposed method is independent to the path-dependency of the materials. An assumed strain method is employed to formulate the discrete equilibrium equations, and the smoothed deformation gradient serves as the stabilization mechanism in the nodally integrated variational equation. Eigenvalue analysis demonstrated that the proposed strain smoothing provides a stabilization to the nodally integrated discrete equations. By employing Lagrangian shape functions, the computation of smoothed gradient matrix for deformation gradient is only necessary in the initial stage, and it can be stored and reused in the subsequent load steps. A significant gain in computational efficiency is achieved, as well as enhanced accuracy, in comparison with the meshfree solution using Gauss integration. The performance of the proposed method is shown to be quite robust in dealing with irregular discretization.
  Manuscript Submission Date: Mon Nov 12 12:09:53 2001
  Paper: jschen
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• J. S. Chen, W. Han, Y. You, X. Meng, Reproducing Kernel Interpolation Without Finite Element Enrichment
  Keywords: Reproducing Kernel Approximation, Reproducing Kernel Interpolation, Galerkin Meshfree Methods, Boundary Condition Treatments, Kronecker Delta Properties
  Abstract: A general formulation for developing reproducing kernel interpolation is presented. This is based on the coupling of a primitive function and an enrichment function. The primitive function introduces discrete Kronecker delta properties, while the enrichment function constitutes reproducing conditions. A necessary condition for obtaining a reproducing kernel interpolation function is an orthogonality condition between the vector of enrichment functions and the vector of shifted monomial functions at the discrete points. A normalized kernel function with relative small support is employed as the primitive function. This approach does not employ a finite element shape function and therefore the interpolation function can be arbitrarily smooth. To maintain the convergence properties of the original reproducing kernel approximation, a mixed interpolation is introduced. A rigorous error analysis is provided for the proposed method. Optimal order error estimates are shown for the meshfree interpolation in any Sobolev norms. Optimal order convergence is maintained when the proposed method is employed to solve one-dimensional boundary value problems. Numerical experiments are done demonstrating the theoretical error estimates. The performance of the method in illustrated in several sample problems.
  Manuscript Submission Date: Mon Nov 12 12:24:20 2001
  Paper: jschen_a
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• Shaofan Li, Wing Kam Liu, Meshfree and Particle Methods and Their Applications
  Keywords:
  Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics (SPH) is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been active research area in recent years, are reviewed. Third, some applications of molecular dynamics (MD) in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, shear bands, incompressible as well as compressible flows; multiscale methods; and nano-scale mechanics.
  Manuscript Submission Date: Wed Nov 7 15:32:17 2001
  Paper: wingkamliu
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• Su Hao, Harold S. Park, Wing Kam Liu , Moving Particle Finite Element Method
  Keywords:
  Abstract: This paper presents the fundamental concepts behind the moving particle finite element method (MPFEM), which combines salient features of the finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems.
  Manuscript Submission Date: Wed Nov 7 16:06:06 2001
  Paper: wingkamliu_a
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• Gregory Wagner, Wing Kam Liu , Hierarchical enrichment for bridging scales and meshfree boundary conditions
  Keywords:
  Abstract: The finite element method, when used with a basis made up of piecewise polynomials, often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near-singularities. Enrichment of the basis with additional functions, obtained through analytical or experimental means, can allow for a coarser mesh and more accurate solution. We introduce an enrichment scheme in which an interaction or ``bridging'' scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions, in effect making the enrichment hierarchical. This separation of scales allows the simple application of essential boundary conditions. It also allows a quantification of the effects of the enrichment, leading to strategies for error estimation and control of the stiffness matrix condition number. We also find that this formulation allows for the simple application of essential boundary conditions for meshfree shape functions, which are notoriously problematic. We find that for multiple dimensions, care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary.
  Manuscript Submission Date: Mon Nov 12 14:37:39 2001
  Paper: wingkamliu_b
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• Wing Kam Liu, Su Hao, Ted Belytschko, ShaoFan Li, Chin Tang Chang , Multi-Scale Methods
  Keywords:
  Abstract: In this paper four multiple scale methods are proposed. The meshless hierar- chical partition of unity is used as a multiple scale basis. The multiple scale analysis with the introduction of a dilation parameter to perform multiresolution analysis is discussed. The multiple field based on a 1D gradient plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening/localization problems. A nonlocal (smoothing) particle integration procedure with its multiple scale analysis are then developed. These techniques are described in the context of the reproducing kernel particle method. Results are presented for elastic-plastic one-dimensional prob- lems and 2-D large deformation strain localization problems to illustrate the effectiveness of these methods.
  Manuscript Submission Date: Mon Nov 12 14:41:04 2001
  Paper: wingkamliu_c
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