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Simulation of bulk metal forming by means of finite integral mesh free methods

PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2005年第9期219卷 949-963页

作者： Li, CS Xiong, SW Rodrigues, JMC Martins, PAF Univ Tecn Lisboa Inst Super Tecn Dept Engn Mecan P-1049001 Lisbon Portugal Northeastern Univ State Key Lab Rolling & Automat Shenyang Peoples R China Northwestern Univ Dept Mech Engn Evanston IL 60208 USA

This paper draws from the fundamentals of the finite integral mesh free representation methods and of the rigid-plastic formulation for slightly compressible materials to the main aspects of computer implementation and modelling of bulk-metal forming processes. Fundamental research and development is based on the reproducing kernel particle method (RKPM) and the corrected smoothed particle hydrodynamics (CSPH) method. Special emphasis is placed on a wide range of theoretical and numerical subjects such as discretization procedures, numerical integration of the system matrices derived from the weak form, relief of volumetric locking, geometrical update of the deforming workpiece, and treatment of the frictional contact interface between the workpiece and tooling. The overall presentation is supported by cold forming experimental parts based on the upsetting of bars and the side pressing of rods under laboratory-controlled conditions. Comparisons between RKPM and CSPH predictions, finite element computations, and experimental results comprise a wide range of topics such as material flow, geometry, forming load, and distribution of strain. The agreement between mesh free methods, finite elements, and experimental results is good.

关键词： bulk metal forming reproducing kernel particle method corrected smoothed particle hydrodynamics method finite element method experimentation

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Meshfree method for 3D bulk forming analysis with lower order integration scheme

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2004年第10期28卷 1283-1292页

作者： Li, GY Sidibe, K Liu, GR Hunan Univ Coll Mech & Automot Engn Changsha 410082 Hunan Peoples R China

Three-dimensional (3D) bulk forming simulation by reproducing kernel particle method is presented in this paper. For increasing computational efficiency a lower order integration scheme is proposed and a general benchmark test for explicit non-linear program is developed, to verify the correctness and the accuracy of the present scheme. A particle to segment contact algorithm for treatment of the contact between deformable and rigid bodies is also presented. The algorithm is found to be very effective and suitable for 3D bulk forming analysis. (C) 2004 Elsevier Ltd. All fights reserved.

关键词： reproducing kernel particle method reduced integration benchmark test contact bulk forming

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Extended immersed boundary method using FEM and RKPM

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2004年第12-14期193卷 1305-1321页

作者： Wang, XD Liu, WK Polytech Univ Dept Mech Engn Brooklyn NY 11201 USA Northwestern Univ Dept Engn Mech Evanston IL 60208 USA

The proposed extended immersed boundary method (EIBM) has several distinct features in comparison with the immersed boundary (IB) method. In the IB method, the interaction between the immersed elastic boundary and the surrounding viscous fluid is replaced with an equivalent body force distribution within the fluid domain. The key ingredient of the IB method is the enforcement of the energy input from the equivalent body force into the fluid domain to be the same (at all time) as that of the elastic forces within the IB. In EIBM, instead of the volumeless immersed elastic boundary, we consider the submerged elastic solid which occupies a finite volume within the fluid domain. In particular, we replace the kinematic and dynamic matching of the fluid-solid interface and the effect of the submerged solid with a judiciously chosen collection of equivalent nodal forces calculated in the context of finite element formulations. The employment of the finite element representation enables a realistic stress analysis for the submerged solid subject to large deformations. Finally, in EIBM, we also replace the discretized delta function commonly used in the IB method with the kernel functions in meshless reproducing kernel particle method (RKPM). With this improvement, using the same finite support domain, we could improve the discretized delta function from C-1 to C-n continuity, where n is chosen according to the required smoothness and resolution of such functions, and more importantly, enables the use of non-uniform meshing in the fluid domain. These extensions may eventually open doors to the modelling of complex biological fluid involving molecular, cellular, and flexible vessel-flow interactions. (C) 2004 Elsevier B.V. All rights reserved.

关键词： extended immersed boundary method immersed boundary method finite element method reproducing kernel particle method meshfree method fluid-structure interaction biofluid particulate flow

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Immersed finite element method

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2004年第21-22期193卷 2051-2067页

作者： Zhang, L Gerstenberger, A Wang, XD Liu, WK Northwestern Univ Inst Technol Dept Mech Engn Evanston IL 60208 USA Polytech Univ MetroTech Ctr 6 Dept Mech Engn Brooklyn NY 11201 USA

In this paper, the immersed finite element method (IFEM) is proposed for the solution Of Complex fluid and deformable structure interaction problems encountered in many physical models. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans over the entire computational domain. Hence, the mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub-domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method (RKPM) delta function. In comparison with the immersed boundary (1B) method, the higher-ordered RKPM delta function enables the fluid domain to have non-uniform spatial meshes with arbitrary geometries and boundary conditions. The use Of Such kernel functions may eventually open doors to multi-scale and multi-resolution modelings of complex fluid-structure interaction problems. Rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method. The results compare well with the experimental data. To the authors' knowledge, these are the first solutions that deal with particulate flows with very flexible solids. (C) 2004 Elsevier B.V. All rights reserved.

关键词： immersed finite element method reproducing kernel particle method fluid-structure interaction particulate flow immersed boundary method

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Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN FLUIDS 2004年第12期46卷 1237-1252页

作者： Liu, YL Zhang, L Wang, XD Liu, WK Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Tulane Univ Dept Mech Engn New Orleans LA 70118 USA Dept Math Sci Newark NJ 07102 USA

The red blood cell (RBC) aggregation plays an important role in many physiological phenomena, in particular the atherosclerosis and thrombotic processes. In this research, we introduce a new modelling technique that couples Navier-Stokes equations with protein molecular dynamics to investigate the behaviours of RBC aggregates and their effects on the blood theology. In essence, the Lagrangian solid mesh, which represents the immersed deformable cells, is set to move on top of a background Eulerian mesh. The effects of cell-cell interaction (adhesive/repulsive) and hydrodynamic forces on RBC aggregates are studied by introducing equivalent protein molecular potentials into the immersed finite element method. The aggregation of red blood cells in quiescent fluids is simulated. The de-aggregation of a RBC cluster at different shear rates is also investigated to provide an explanation of the shear-rate-dependence of the blood viscoelastic properties. Finally, the influences of cell-cell interaction, RBC rigidity, and vessel geometry are addressed in a series of test cases with deformable cells (normal and sickle RBCs) passing through micro- and capillary vessels. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： Immersed Finite Element method reproducing kernel particle method fluid-structure interaction Navier-Stokes equations protein molecular dynamics red blood cell aggregation coagulation microcirculation capillary

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Numerical method for shape optimization using meshfree method

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2003年第6期24卷 418-429页

作者： Kim, NH Choi, KK Botkin, ME Univ Florida Dept Mech Engn Gainesville FL 32611 USA Univ Iowa Ctr Comp Aided Design Iowa City IA 52242 USA GM Corp Vehicle Anal & Dynam R&D & Planning Warren MI 48090 USA

A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element-based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.

关键词： design sensitivity analysis shape optimization meshfree method reproducing kernel particle method

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Analysis of rectangular laminated composite plates via FSDT meshless method

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2002年第7期44卷 1275-1293页

作者： Wang, J Liew, KM Tan, MJ Rajendran, S Nanyang Technol Univ Sch Mech & Prod Engn Ctr Adv Numer Engn Simulat Singapore 639798 Singapore

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： meshless reproducing kernel particle method RKPM bending free vibration buckling laminated composite plates first-order shear defori-nation plate theory

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Characteristics of semi- and full discretization of stabilized Galerkin meshfree method

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2002年第10期38卷 999-1012页

作者： You, Y Chen, JS Voth, TE Univ Calif Los Angeles Dept Civil & Environm Engn Los Angeles CA 90095 USA Sandia Natl Labs Thermal Sci Dept Albuquerque NM 87185 USA

Stabilized conforming nodal integration (SCNI) has been developed to enhance computational efficiency of Galerkin meshfree methods. This paper employs von Neumann analyses to study the spatial semi-discretization of Galerkin meshfree methods using SCNI. Two model problems were presented with respect to the normalized phase speed and group speed for the wave equation, and normalized diffusivity for the heat equation. Both consistent and lumped mass (capacity) discretizations are considered in the study. The transient properties in the full discretization of the two model problems were also analyzed. The results show superior dispersion behavior in meshfree methods integrated by SCNI compared to the Gauss integration when consistent mass (capacity) matrix is employed in the discretization. For the lumped mass case, SCNI performance is comparable to that of the Gauss integration, but exhibits considerable reduction of computational time. (C) 2002 Elsevier Science B.V.. All rights reserved.

关键词： stabilized conforming nodal integration meshfree methods reproducing kernel particle method discretization error

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Effective models for prediction of springback in flanging

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JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME 2001年第4期123卷 456-461页

作者： Song, N Qian, D Cao, J Liu, WK Li, SF Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Univ Calif Berkeley Dept Civil & Environm Engn SEMM Grp Berkeley CA 94720 USA

A study on the prediction of springback angle is presented, with focus on the straight flanging operation. The objective of this work is to evaluate the reliability of different methods of prediction. An experiment of straight flanging operation is conducted. Major prediction approaches such as analytical model, numerical simulation using the Finite Element method (FEM) and the Meshfree method using the reproducing kernel particle methods (RKPM) are discussed. A set of sample problems is computed and comparisons are made with the experiment. The numerical analysis shows that the prediction from the 3D meshfree contact code matches well with the data from the FEM 2D solid model. A material property described by the kinematic hardening law provides a better prediction of springback than the isotropic hardening law.

关键词： metal forming flanging springback meshfree method kinematic hardening reproducing kernel particle method

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reproducing kernel hierarchical partition of unity, part II - Applications

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 1999年第3期45卷 289-317页

作者： Li, SF Liu, WK Northwestern Univ Dept Engn Mech Evanston IL 60208 USA

In this part of the work, the meshless hierarchical partition of unity proposed in [1], referred here as Part I, is used as a multiple scale basis in numerical computations to solve practical problems. The applications discussed in the present work fall into two categories: (1) a wavelet adaptivity refinement procedure;and (2) a so-called wavelet Petrov-Galerkin procedure. In the applications of wavelet adaptivity, the hierarchical reproducing kernels are used as a multiple scale basis to compute the numerical solutions of the Helmholtz equation, a model equation of wave propagation problems, and to simulate shear band formation in an elasto-viscoplastic material, a problem dictated by the presence of the high gradient deformation. In both numerical experiments, numerical solutions with high resolution are obtained by inserting the wavelet-like basis into the primary interpolation function basis, a process that may be viewed as a spectral p-type refinement. By using the interpolant that has synchronized convergence property as a weighting function, a wavelet Petrov-Galerkin procedure is proposed to stabilize computations of some pathological problems in numerical computations, such as advection-diffusion problems and Stokes' flow problem;it offers an alternative procedure in stabilized methods and also provides some insight, or new interpretation of the method. Detailed analysis has been carried out on the stability and convergence of the wavelet Petrov-Galerkin method. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： meshless methods reproducing kernel particle method partition of unity p-adaptivity wavelet Petrov-Galerkin method

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