In this paper, a multi-scale meshfree-enriched finite element formulation is presented for the analysis of acoustic wave propagation problem. The scale splitting in this formulation is based on the Variational Multi-scale (VMS) method. While the standard finite element polynomials are used to represent the coarse scales, the approximation of fine-scale solution is defined globally using the meshfree enrichments generated from the Generalized Meshfree (GMF) approximation. The resultant fine-scale
approximations satisfy the homogenous Dirichlet boundary conditions and behave as the \"global residual-free\" bubbles for the enrichments in the oscillatory type of Helmholtz solutions. Numerical examples in one dimension and two dimensional cases are analyzed to demonstrate the accuracy of the present formulation and comparison is made to the analytical and two finite element solutions.
acoustic; multi-scale; finite element; Helmholtz; meshfree
C.T. Wu and Wei Hu : Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA
A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal
representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.
In this study, atomistic simulations are performed to study the effect of Al solute on the behaviour of edge dislocation in Mg alloys. After the dissociation of an Mg basal edge dislocation into two Shockley partials using molecular mechanics, the interaction between the dislocation and Al solute at different temperatures is studied using molecular dynamics. It appears from the simulations that the critical shear stress increases with the Al solute concentration. Comparing with the solute effect at T = 0 K, however, the critical shear stress at a finite temperature is lower since the kinetic energy of the atoms can help the dislocation conquer the energy barriers created by the Al atoms. The velocity of the edge dislocation decreases as the Al concentration increases when the external shear stress is relatively small regardless of temperature. The Al concentration effect on the dislocation velocity is not significant at very high shear stress level when the solute concentration is below 4.0 at%. Drag coefficient B increases with the Al concentration when the stress to temperature ratio is below 0.3 MPa/K, although the effect is more significant at low temperatures.
In this paper, a meshfree shell adaptive procedure is developed for the applications in the sheet metal forming simulation. The meshfree shell formulation is based on the first-order shear deformable shell theory and utilizes the degenerated continuum and updated Lagrangian approach for the nonlinear analysis. For the sheet metal forming simulation, an h-type adaptivity based on the meshfree background cells is considered and a geometric error indicator is adopted. The enriched nodes in adaptivity are added to the centroids of the adaptive cells and their shape functions are computed using a first-order generalized
meshfree (GMF) convex approximation. The GMF convex approximation provides a smooth and non-negative shape function that vanishes at the boundary, thus the enriched nodes have no influence outside the adapted cells and only the shape functions within the adaptive cells need to be re-computed. Based on this concept, a multi-level refinement procedure is developed which does not require the constraint equations to enforce the compatibility. With this approach the adaptive solution maintains the order of meshfree approximation with least computational cost. Two numerical examples are presented to demonstrate the
performance of the proposed method in the adaptive shell analysis.
meshfree; convex; shell; adaptivity; metal forming
Yong Guo , C.T. Wu : Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA
C.K. Park : National Crash Analysis Center (NCAC), The George Washington University, 45085 University Drive, Ashburn, VA 20147, USA
This paper presented an investigation of macromolecular suspension in a grooved channel by using the dissipative particle dynamics (DPD) with finitely extensible non-linear elastic (FENE) bead spring chains model. Before studying the movement and evolution of macromolecules, the DPD method was first validated by modeling the simple fluid flow in the grooved channel. For both simple fluid flow and
macromolecular suspension, the flow fields were analyzed in detail. It is found that the structure of the grooved channel with sudden contraction and expansion strongly affects the velocity distribution. As the width of the channel reduces, the horizontal velocity increases simultaneously. Vortices can also be found at the top and bottom corners behind the contraction section. For macromolecular suspension, the macromolecular chains influence velocity and density distribution rather than the temperature and pressure. Macromolecules tend to drag simple fluid particles, reducing the velocity with density and velocity fluctuations. Particle trajectories and evolution of macromolecular conformation were investigated. The structure of the grooved channel with sudden contraction and expansion significantly influence the evolution of macromolecular conformation, while macromolecules display adaptivity to adjust their own conformation and angle to suit the structure so as to pass the channel smoothly.
dissipative particle dynamics; macromolecular suspension; grooved micro-channel
L.W. Zhou, M.B. Liu : Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
J.Z. Chang : School of Mechatronic Engineering, North University of China, Taiyuan 030051, China
Meshfree methods are known to have the capability to overcome the strict regularization requirements and numerical instabilities that encumber the finite element method (FEM) in large deformation problems. They are also more naturally suited for problems involving material perforation and fragmentation. To take advantage of the high efficiency of FEM and high accuracy of meshfree methods, a coupled finite element (FE) and reproducing kernel (RK, one of the meshfree approximations) formulation
is described in this paper. The coupling of FE and RK approximation is implemented in an evolutionary fashion, where the extent and location of the evolution is dependent on a triggering criteria provided by the material constitutive laws. To enhance computational efficiency, Gauss quadrature is applied to integrate both FE and RK domains so that no state variable transfer is required when mesh conversion is performed. To control the hourglassing that might occur with 1-point integrated hexahedral grids, viscous type hourglass control is implemented. Meanwhile, the FEM version of the K&C concrete (KCC) model was modified to make it applicable in both FE and RK formulations. Results using this code and the KCC model are shown for the modeling of concrete responses under quasi-static, blast and impact loadings. These analyses demonstrate that fragmentation phenomena of the sort commonly observed under blast and impact loadings of concrete structures was able to be realistically captured by the coupled formulation.
Reproducing Kernel (RK); Finite Element (FE); coupled FE/RK; fragmentation; concrete
Youcai Wu, Hyung-Jin Choi and John E. Crawford : Karagozian & Case (K&C), 700 N. Brand Blvd., Suite 700, Glendale, CA 91203, USA
A fundamental trend of processor architecture evolving towards exaflops is fast increasing floating point performance (so-called \"free\" flops) accompanied by much slowly increasing memory and network bandwidth. In order to fully enjoy the \"free\" flops, a numerical algorithm of PDEs should request more flops per byte or increase arithmetic intensity. A meshfree/GFEM approximation can be the class of the algorithm. It is shown in a GFEM without extra dof that the kind of approximation takes advantages of the high performance of manycore GPUs by a high accuracy of approximation; the \"expensive\" method is found to be reversely hardware-efficient on the emerging architecture of manycore.
meshfree; GFEM; manycore; co-design; exascale computing
Rong Tian : Institute of Computing Technology, Chinese Academy of Sciences, Kexueyuan Nanlu 6, Haidian, Beijing 100190, China
An incompressible smoothed particle hydrodynamics (ISPH) method based on the incremental pressure projection method is developed in this study. The Rayleigh-Benard convection in a square enclosure is used as a validation case and the results obtained by the proposed ISPH model are compared to
the benchmark solutions. The comparison shows that the established ISPH method has a good performance in terms of accuracy. Subsequently, the proposed ISPH method is employed to simulate natural convection from a heated cylinder in a square enclosure. It shows that the predictions obtained by the ISPH method are in good agreements with the results obtained by previous studies using alternative numerical methods. A rotating and heated cylinder is also considered to study the effect of the rotation on the heat transfer process in the enclosure space. The numerical results show that for a square enclosure at , the addition of kinetic energy in the form of rotation does not enhance the heat transfer process. The method is also applied to simulate forced convection from a circular cylinder in an unbounded uniform flow. In terms of results, it turns out that the proposed ISPH model is capable to simulate heat transfer problems with the complex and moving boundaries.
In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear
formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction
with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the
integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A
modified variational formulation using the smoothed deformation gradient is developed for path-dependent
material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in
the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis.
meshfree; finite element; nonlinear; near-incompressible; plasticity; contact
Wei Huand C.T. Wu : Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA
The use of lightweight materials has been steadily increasing in the automotive industry, and
presents new challenges to material joining. Among many joining processes, self-piercing riveting (SPR) is
particularly promising for joining lightweight materials (such as aluminum alloys) and dissimilar materials
(such as steel to Al, and metal to polymer). However, to establish a process window for optimal joint
performance, it often requires a long trial-and-error testing of the SPR process. This is because current state
of the art in numerical analysis still cannot effectively resolve the problems of severe material distortion and
separation in the SPR simulation. This paper presents a coupled meshfree/finite element with a moving
boundary algorithm to overcome these numerical difficulties. The simulation results are compared with
physical measurements to demonstrate the effectiveness of the present method.
meshfree method; element free galerkin method; finite element method; moving boundary;
self piercing riveting
1Research and Development Center, General Motors R&D Wayne Cai, Hui-Ping Wang: Center, 30500 Mound Road, Warren,
MI 48090, USA
C.T. Wu: Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore,CA 94550, USA