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Three dimensional meshfree analysis for time-Caputo and space-Laplacian fractional diffusion equation

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2023年 157卷 553-564页

作者： Lin, Zeng Liu, Fawang Wu, Junchao Wang, Dongdong Gu, Yuantong Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Peoples R China Queensland Univ Technol Sch Math Sci GPO Box 2434 Brisbane Qld 4001 Australia Fuzhou Univ Sch Math & Stat Fuzhou 350116 Peoples R China Huaqiao Univ Coll Civil Engn Key Lab Intelligent Infrastructure & Monitoring Fu Xiamen 361021 Peoples R China Xiamen Univ Dept Civil Engn Fujian Key Lab Digital Simulat Coastal Civil Engn Xiamen 361005 Peoples R China Queensland Univ Technol Sch Mech Med & Proc Engn GPO Box 2434 Brisbane Qld 4001 Australia

Numerical exploration of spatial fractional differential equations in three dimensions is not trivial due to their complexity, especially for complicated problem domains. In this work, the time-Caputo and space-Laplacian fractional diffusion equations in three dimensions are analyzed using a meshfree technique. In the temporal dimension, the classical L1 finite difference scheme is used to approach the Caputo fractional derivative. The spatial discretization is realized by a three dimensional reproducing kernel particle method (RKPM), which can eliminate the dependence of shape functions on certain meshes. Therefore RKPM is very suitable to approximate the field variable in complicated three dimensional domains compared with other mesh dependent methods. For the purpose of increasing the computational efficiency, the stabilized conforming nodal integration (SCNI) and lumped mass matrix techniques are adopted in the Galerkin meshfree formulation. In the proposed method, the tedious derivatives computing for meshfree shape functions, numerical integration for Galerkin weak form and time-consuming inverse calculating for the large size mass matrix are all realized by more efficient approaches comparing with the conventional Galerkin RKPM. Several numerical examples in various domains with structured and unstructured discretization are studied to demonstrate the proposed methodology, and the results show very favorable performance of the proposed method regarding the accuracy and effectiveness.

关键词： Fractional diffusion equation reproducing kernel particle method Stabilized conforming nodal integration Lumped mass matrix

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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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A 3D meshless radial basis reproducing kernel particle model for elastoplastic analysis of temperature-dependent FG plates resting on Winkler/Pasternak foundation

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2022年 144卷 127-144页

作者： Vaghefi, Reza Karimzadeh, Ali Fasa Univ Dept Mech Engn Fasa Iran

For the first time, a three-dimensional (3D) meshless approach based on the radial basis reproducing kernel particle method (RRKPM) is developed to scrutinize the nonlinear thermo-elastoplastic bending response of temperature-dependent functionally graded (FG) plates resting on Winkler/Pasternak foundation under a com-bination of mechanical and thermal loads. The modified rule of mixtures is employed to locally evaluate the effective temperature-dependent parameters of the functionally graded material (FGM). To describe the plastic behavior of the FG plate, the von Mises yield criterion, isotropic strain hardening, and the Prandtl-Reuss flow rule are adapted. To demonstrate the accuracy and efficiency of the present method, the outcomes are compared with other existing numerical and analytical results, which shows an excellent agreement. Detailed studies have been conducted on the scaling factor, shape parameter and nodal distribution for finding their desired values. Furthermore, the effect of significant parameters such as material gradient, elastic foundation parameters, thickness ratio, and boundary conditions on the bending response of FG plates has been investigated.

关键词： Thermo-elastoplastic analysis reproducing kernel particle method Radial basis function Functionally graded plate Temperature -dependent material properties

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A stabilized quasi and bending consistent meshfree Galerkin formulation for Reissner-Mindlin plates

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COMPUTATIONAL MECHANICS 2022年第6期70卷 1211-1239页

作者： Huang, Tsung-Hui Wei, Yen-Ling Natl Tsing Hua Univ Dept Power Mech Engn Hsinchu Taiwan

The state-of-the-art locking-free meshfree Galerkin formulation for modeling the Reissner-Mindlin plate problems is plagued by the following issues: (1) the requirement of a large enough kernel support size in avoiding kernel instability because of the quadratic basis in meeting the Kirchhoff mode reproducing condition, as well as (2) the tedious construction of the conforming representative domains and the smoothed strain in the stabilized conforming integration scheme. This study introduces an efficient and stabilized approach that circumvents the above-mentioned issues. A quasi-consistent reproducing kernel approximation is first developed to enable a smaller kernel support size to be used without the moment matrix singularity issue under a controllable loss of completeness;thus, the approximation construction is accelerated. Then, a bending consistent nodal integration method is proposed where the bending consistency in Galerkin formulation is achieved via an assumed strain approach without using the conforming cell. A variational multiscale stabilization method from our earlier research is implemented to avoid low energy instability while maintaining the locking-free property. The performance of the present formulation is validated in several benchmark problems.

关键词： reproducing kernel particle method Stabilized bending consistent nodal integration Quasi-consistent approximation Reissner-Mindlin plate

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Meshless numerical solution for nonlocal integral differentiation equation with application in peridynamics

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2022年第0期144卷 569-582页

作者： Yao, Wu -Wen Zhou, Xiao-Ping Chongqing Univ Sch Civil Engn Chongqing 400045 Peoples R China

The mid-point quadrature rule is often used to solve the nonlocal integral differentiation equations, in which a central material point is used to calculate the integral of the subdomain in the meshless geometry. However, it can only achieve the linear approximation and the first order convergence rate, and it is only accurate enough when the entire cell overlaps with the neighborhood of a material point. In this paper, to achieve the higher precision and the higher rate of convergence speed, a novel coupling method of reproducing kernel particle method and Gaussian-Legendre quadrature scheme is proposed to solve the nonlocal integral differentiation equations in the meshless geometry, in which the mid-point quadrature scheme is replaced with Gauss quad-rature scheme to calculate the integral of the subdomain in the meshless geometry, the reproducing kernel particle method is employed to construct the shape functions for material points in the nonlocal model, and to approximate the value of the Gaussian quadrature node. Moreover, the meshless solution for the peridynamic equation is derived detailedly based on the proposed method. Compared with the traditional meshless solution for the nonlocal equations, the proposed solution has higher precision and higher rate of convergence speed in different problems. The numerical results demonstrate improved results in both mathematics and mechanical problems using the proposed method.

关键词： Nonlocal integral differentiation equations Meshless numerical solution reproducing kernel particle method Gaussian-Legendre quadrature Peridynamics

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A variational multiscale stabilized and locking-free meshfree formulation for Reissner-Mindlin plate problems

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COMPUTATIONAL MECHANICS 2022年第1期69卷 59-93页

作者： Huang, Tsung-Hui Natl Tsing Hua Univ Dept Power Mech Engn Hsinchu Taiwan

In this study, a variational multiscale stabilized locking-free meshfree formulation is introduced for modeling Reissner-Mindlin plate problems under arbitrary plate thickness. Under this framework, the plate quantities are decoupled into coarse-scale and fine-scale components in the variational equations, where the fine-scale solution represents a correction to the residual of the coarse-scale equations that can be solved by an effective collocation-type approach with an approximation method meeting locking free conditions. The substitution of fine-scale solutions in the coarse-scale system leads to a residual-based Galerkin formulation. In the proposed framework, the reproducing kernel approximation, as well as the smoothed gradient and divergence, are adopted to ensure the bending exactness in the Galerkin formulation. The multiscale approach is also beneficial for problems exhibiting localized phenomena. The effectiveness of the proposed method is tested by solving a series of numerical examples and compared with classical methods.

关键词： reproducing kernel particle method Stabilized nodal integration Variational multiscale method Shear locking Reissner-Mindlin plate

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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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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 fracture mechanics study of stress resultant intensity factors in stiffened panels employing RKPM meshfree FSDT modeling

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THIN-WALLED STRUCTURES 2024年 197卷

作者： Tanaka, Satoyuki Takata, Akihiro Matsuoka, Naoki Sadamoto, Shota Hiroshima Univ Grad Sch Adv Sci & Engn 4-1 Kagamiyama 1 Chome Higashihiroshima 7398527 Japan Fujitsu Ltd 4-1-1 KamikodanakaNakahara Ku Kawasaki Kanagawa 2118588 Japan

Panel cracking for stiffened panels is investigated based on linear elastic fracture mechanics. Meshfree flat shell formulation and fracture modeling are employed. After investigating stress distribution of the intact stiffened panel, the mode -I and mixed -mode crackings are studied using the stress resultant intensity factors (SRIFs). When the crack tip approaches to the stiffener, deformation around the crack is suppressed due to presence of the stiffeners. The mechanical behaviors are carefully examined by changing crack length, loading conditions and thickness of the main panel and stiffeners. Quantitative evaluation of SRIFs is addressed by comparing with the reference solutions. An in-depth discussion is provided for the meshfree modeling of the panel cracking in the stiffened panels. This series studies are useful for examining crack arrest effect of the stiffened panel due to presence of the stiffeners.

关键词： Stiffened panel Stress intensity factor Meshfree modeling reproducing kernel particle method

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Static behavior of ribbed folded plate roof under vertical uniform load-Experimental study and meshfree method analysis

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STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS 2024年第4期33卷 e2079-e2079页

作者： Sun, Renzhong Ma, Kejian Zhang, Huagang Yu, Fang Fang, Qiang Guizhou Univ Res Ctr Space Struct Guiyang Peoples R China Guizhou Univ Coll Civil Engn Guiyang Peoples R China Guizhou Prov Key Lab Struct Engn Guiyang Peoples R China Guizhou Prov Key Lab Struct Engn Guiyang 550025 Peoples R China

Folded plate roofs are widely used in building roofs due to their light weight and high stiffness. However, traditional folded plate roofs are often limited in application due to insufficient stiffness under the current trend of pursuing larger-span roofs. Ribbed folded plate roofs can effectively solve this problem because ribs not only increase the stiffness of the roof and reduce stress concentration, but they are also easy to be formed into various shapes to meet different needs for buildings. Therefore, the detailed analysis was carried out on a reinforced concrete ribbed folded plate roof (RCRFR) under the vertical uniform load to investigate its static behavior. The bearing capacity, failure mode, load-displacement relationship, and strain variation were obtained through the test. Additionally, based on the finite element (FE) method, not only a comparison was conducted between RCRFR and reinforced concrete ribless folded plate roof (RCLFR), but the influence of material nonlinearity and geometric nonlinearity on the structure was also investigated. Moreover, the bending characteristics of RCRFR under design load were analyzed based on the reproducing kernel particle method. The experimental results showed that this structure had good mechanical properties within the design load. In the overload stage, the concrete on the underside of the structure was severely damaged. Furthermore, the yielding of the ribbed plate's reinforcing bars caused the increased vertical deformation difference between the ribbed plate and the top chord, and the ribbed plate and the central ridge beam. Eventually, the failure of the anchorage of the ribbed plate's reinforcing bars anchored in the central ridge beam and the top chord led to the loss of structural load-bearing capacity. The FE analysis results demonstrated that ribs enhance the stiffness of the structure, with material nonlinearity having the primary impact and geometric nonlinearity exerting a secondary effect. The mes

关键词： deflection analysis finite element reinforced concrete reproducing kernel particle method ribbed folded plate roof strain analysis

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