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A unified approach to meshless analysis of thin to moderately thick plates based on a shear-locking-free Mindlin theory formulation

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THIN-WALLED STRUCTURES 2018年第Mar.期124卷 161-179页

作者： Khezri, M. Gharib, M. Rasmussen, K. J. R. Univ Sydney Sch Civil Engn Sydney NSW 2006 Australia Univ New South Wales Sch Civil & Environm Engn Sydney NSW 2052 Australia

The conventional numerical approximation of Mindlin plate equations can lead to erroneous solutions for thin plates. The so-called shear-locking problem has been well studied in the context of the finite element method (FEM) whereas the development of numerical formulations for its successful elimination in meshfree methods is still a subject of intensive research. This paper studies the effectiveness of some of the most commonly adopted techniques for the reduction of shear-locking and presents the application of a shear-locking-free formulation based on fast-order Mindlin plate theory. In this modified formulation, the shear strains are incorporated as degrees of freedom (DOFs) in lieu of the rotational DOFs in the conventional Mindlin theory formulation. A straightforward transformation technique is presented for the enforcement of boundary conditions and comparisons are made with available analytical and numerical solutions. The generalised reproducing kernel particle method (RKPM) is adopted as the numerical tool and a series of numerical examples are presented to demonstrate the accuracy and performance of the presented method.

关键词： Meshless reproducing kernel particle method Plate bending Shear-locking Modified Mindlin theory

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Free vibration analysis of thin-walled folded structures employing Galerkin-based RKPM and stabilized nodal integration methods

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2024年 163卷 308-317页

作者： Tanaka, Satoyuki Ejima, Shion Wang, Hanlin Sadamoto, Shota Hiroshima Univ Grad Sch Adv Sci & Engn 4-1Kagamiyama 1 Chome Higashihiroshima 7398527 Japan Fujitsu Ltd 4-1-1 KamikodanakaNakahara Ku Kawasaki Kanagawa 2118588 Japan

A Galerkin-based meshfree flat shell formulation is chosen to study natural frequency and eigenmode of thin-walled folded structures. reproducing kernel is used as the interpolation function. Stabilized conforming nodal integration is employed for numerical integration of the weak form. Additionally, sub-domain stabilized conforming integration is adopted for the folded region to integrate the stiffness matrix accurately. The first order shear deformation theory is utilized considering in-plane deformation, out-of-plane deformation and drilling components. The singular kernel function is introduced to effectively handle the folded geometry. An advanced free vibration simulation can be achieved. Accuracy and effectiveness of the meshfree modeling are demonstrated through the numerical examples.

关键词： Folded shell structure Free vibration reproducing kernel particle method Nodal integration First order shear deformation theory

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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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Content-Dependent Nonlinear Vibration of Composite Plates Reinforced with Carbon Nanotubes

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JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES 2022年第4期10卷 1253-1264页

作者： Zhang, W. He, L. J. Wang, J. F. Beijing Univ Technol Fac Mat & Mfg Beijing Key Lab Nonlinear Vibrat & Strength Mech Beijing 100124 Peoples R China

Purpose In this paper, the nonlinear vibration behavior of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates is investigated by meshless method. methods The efficiency parameters, which clearly affect the mechanical properties of the composite materials, are characterized by polynomial expressions for different CNT contents, and applied as the inputs in the vibration analysis of plate structure. Four distributions of CNTs along the thickness of composite plate are considered, namely, the uniform distribution (UD), FG-O, FG-X and FG-V. Based on the classical plate theory and von Karman strain-displacement relation, the governing equations of motion are derived by the virtual displacement principle. Based on the reproducing kernel particle method (RKPM), the discrete governing equations for the vibration of the FG-CNTRC plates are derived. The linearized updated mode (LUM) method is adopted to solve the iteration process of governing equations. Results Numerical results are employed to investigate the effects of boundary condition, aspect ratio, volume fraction and arrangement of CNT on the nonlinear vibration characteristics of composite plates.

关键词： Nonlinear vibration Carbon nanotube Functionally graded material Efficiency parameter reproducing kernel particle method

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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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A comparison of linear consistent correction methods for first-order SPH derivatives

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PROCEEDINGS OF THE ACM ON COMPUTER GRAPHICS AND INTERACTIVE TECHNIQUES 2023年第3期6卷 1-20页

作者： Westhofen, Lukas Jeske, Stefan Bender, Jan Rhein Westfal TH Aachen Aachen Germany

Awell-known issue with the widely used Smoothed particle Hydrodynamics (SPH) method is the neighborhood deficiency. Near the surface, the SPH interpolant fails to accurately capture the underlying fields due to a lack of neighboring particles. These errors may introduce ghost forces or other visual artifacts into the simulation. In this work we investigate three different popular methods to correct the first-order spatial derivative SPH operators up to linear accuracy, namely the kernel Gradient Correction (KGC), Moving Least Squares (MLS) and reproducing kernel particle method (RKPM). We provide a thorough, theoretical comparison in which we remark strong resemblance between the aforementioned methods. We support this by an analysis using synthetic test scenarios. Additionally, we apply the correction methods in simulations with boundary handling, viscosity, surface tension, vorticity and elastic solids to showcase the reduction or elimination of common numerical artifacts like ghost forces. Lastly, we show that incorporating the correction algorithms in a state-of-the-art SPH solver only incurs a negligible reduction in computational performance.

关键词： smoothed particle hydrodynamics computer animation moving least squares reproducing kernel particle method

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Pixel-based meshfree modelling of skeletal muscles

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COMPUTER methodS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING-IMAGING AND VISUALIZATION 2016年第2期4卷 73-85页

作者： Chen, Jiun-Shyan Basava, Ramya Rao Zhang, Yantao Csapo, Robert Malis, Vadim Sinha, Usha Hodgson, John Sinha, Shantanu Univ Calif San Diego Dept Struct Engn San Diego CA 92103 USA Univ Calif San Diego Dept Radiol San Diego CA 92103 USA San Diego State Univ Dept Phys San Diego CA 92182 USA Univ Calif Los Angeles Dept Integrat Biol & Physiol Los Angeles CA USA

This paper introduces the meshfree reproducing kernel particle method for 3D image-based modelling of skeletal muscles. This approach allows for construction of simulation model based on pixel data obtained from medical images. The material properties and muscle fibre direction obtained from diffusion tensor imaging (DTI) are input at each pixel point. The reproducing kernel approximation allows a representation of material heterogeneity with smooth transition. A multiphase multichannel level set based segmentation framework is adopted for individual muscle segmentation using magnetic resonance images and DTI. The application of the proposed methods for modelling the human lower leg is demonstrated.

关键词： image-based modelling reproducing kernel particle method 3D skeletal muscle model construction muscle force production image segmentation

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Meshless analysis of bilayer graphene nanoribbon for radio frequency interconnects

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MICRO & NANO LETTERS 2015年第11期10卷 613-616页

作者： Kanthamani, S. Gayathiri, G. Rohini, S. Thiagarajar Coll Engn Dept Elect & Commun Engn Madurai 625015 Tamil Nadu India

Numerical analysis of a bilayer graphene nanoribbon (BLGNR) using the reproducing kernel particle method (RKPM) - a true meshless approach - is reported. Electrostatic analysis of the BLGNR is performed using the RKPM approach. Validation of the structure is executed by comparing the result with an equivalent single conductor model and shows better accordance. Radio frequency (RF) analysis of the BLGNR as the interconnect is studied using advanced design systems with the quasi-static analysis derived through the RKPM method. The simulation results in a return loss of -89.69 dB and transmission loss of -0.00028 dB at 1 THz which is suitable for RF interconnect applications.

关键词： graphene nanoribbons integrated circuit interconnections electrostatics radiofrequency integrated circuits meshless analysis bilayer graphene nanoribbon radiofrequency interconnects reproducing kernel particle method electrostatic analysis equivalent single conductor model

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A Novel Meshfree Analysis of Transient Heat Conduction Problems Using RRKPM

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Computer Modeling in Engineering & Sciences 2022年第6期131卷 1793-1814页

作者： Hongfen Gao Gaofeng Wei College of Intelligent Engineering Shandong Management UniversityJinan250357China School of Mechanical and Automotive Engineering Qilu University of Technology(Shandong Academy of Sciences)Jinan250353China Shandong Institute of Mechanical Design and Research Jinan250353China

By introducing the radial basis functions(RBFs)into the reproducing kernel particle method(RKPM),the calculating accuracy and stability of the RKPM can be improved,and a novel meshfree method of the radial basis RKPM(meshfree RRKPM)is ***,the meshfree RRKPM is applied to transient heat conduction problems(THCP),and the corresponding equations of the meshfree RRKPM for the THCP are *** twopoint time difference scheme is selected to discretize the time of the ***,the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP.

关键词： Transient heat conduction meshfree method reproducing kernel particle method meshfree RRKPM two-point difference method

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A variational multiscale immersed meshfree method for heterogeneous materials

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COMPUTATIONAL MECHANICS 2021年第4期67卷 1059-1097页

作者： Huang, Tsung-Hui Chen, Jiun-Shyan Tupek, Michael R. Beckwith, Frank N. Koester, Jacob J. Fang, H. Eliot Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA Natl Tsing Hua Univ Dept Power Mech Engn Hsinchu Taiwan

We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.

关键词： Heterogeneous material reproducing kernel particle method Variational multiscale immersed method Volumetric constraint

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