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The Isoparametric reproducing kernel particle method for nonlinear deformation of plates

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2014年 42卷 67-76页

作者： Guan, Pai-Chen Sun, Chien-Ting Natl Taiwan Ocean Univ Dept Syst Engn & Naval Architecture Keelung Taiwan

This paper proposed the new Isoparametric reproducing kernel particle method (IsoRKPM) for modeling nonlinear plate and shell deformation problems. The reproducing kernel shape functions are constructed on a two-dimensional parent domain. Following the concept of isoparametric mapping, the RK shape functions are directly used to approximate the plate geometry. A High Order Nodal Integration (HONI) is developed to integrate the Galerkin weak form of the Mindlin plate equilibrium equations. The proposed IsoRKPM with HONI is applied to solve several benchmark problems. Both modal and convergence analyses show that HONI provides more stable and accurate solutions than the nodal integration method. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Meshfree reproducing kernel particle method Nonlinear Plates and shells Numerical integration

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Vibration and buckling analysis of functionally graded beams using reproducing kernel particle method

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SCIENTIA IRANICA 2014年第6期21卷 1896-1906页

作者： Saljooghi, R. Ahmadiana, M. T. Farrahi, G. H. Sharif Univ Technol Sch Mech Engn Tehran Iran Sharif Univ Technol Ctr Excellence Design Robot & Automat Tehran Iran

This paper presents the vibration and buckling analysis of functionally graded beams with different boundary conditions, using the reproducing kernel particle method (RKPM). Vibration of simple Euler-Bernoulli beams using RKPM is already developed and reported in the literature. So far, the modeling of FGM beams using the theoretical method or the finite element technique has not evolved with accurate results for the power law form of FGM with a large power of "n" value. The accuracy of RKPM results is very good and is not sensitive to the n value. The system of equations of motion is derived using Lagrange's method under the assumption of the Euler-Bernoulli beam theory. Boundary conditions of the beam are taken into account using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction, according to the power-law form. RKPM is implemented to obtain the equation of motion and, consequently, natural frequencies and buckling loads of the FGM beam are evaluated. Results are verified for special cases reported in the literature. Considering the displacement of the neutral axis, buckling loads, with respect to length and material distribution, are evaluated. For special cases of homogenous beams, RKPM matches theoretical evaluation with less than one percent error. (C) 2014 Sharif University of Technology. All rights reserved.

关键词： Functionally graded beam reproducing kernel particle method Natural frequencies Critical buckling loads

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Analysis of functionally graded stiffened plates based on FSDT utilizing reproducing kernel particle method

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COMPOSITE STRUCTURES 2014年第1期112卷 231-240页

作者： Ardestani, M. Memar Soltani, B. Shams, Sh. Univ Kashan Fac Mech Engn Kashan *** Isfahan Iran

Using reproducing kernel particle method (RKPM), concentrically and eccentrically functionally graded stiffened plates (FGSPs) are analyzed based on first order shear deformation theory (FSDT). The plates are subjected to uniformly distributed loads with simply supported and clamped boundary conditions. The interactions between the plate and stiffeners are imposed by compatibility equations. Metal-ceramic composition is assumed as the functionally graded material (FGM). Material properties vary through the thickness direction according to the power law of volume fraction. Mori-Tanaka scheme is used to obtain effective material properties. Poisson's ratios of plates and stiffeners are taken to be constant. Full transformation approach is used to enforce essential boundary conditions. Effects of eccentricity of the stiffeners, dimensionless support domain parameter, dimensionless thickness, boundary conditions and the volume fractions of the constituents on the behavior of the stiffened plates are investigated. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Meshfree method reproducing kernel particle method Stiffened plate First order shear deformation theory Full transformation method Functionally graded materials

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On the use of reproducing kernel particle finite strip method in the static, stability and free vibration analysis of FG plates with different boundary conditions and diverse internal supports

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APPLIED MATHEMATICAL MODELLING 2021年 92卷 380-409页

作者： Esfahani, Sadegh Ghamsari Sarrami-Foroushani, Saeid Azhari, Mojtaba Isfahan Univ Technol Dept Civil Engn Esfahan *** Iran

This paper is focused on the application of a novel reproducing kernel particle finite strip method (RKP-FSM) for the static, mechanical and thermal buckling, and free vibration analyses of rectangular functionally graded (FG) plates with different boundary conditions and internal supports. Conventional reproducing kernel particle method (RKPM) is incorporated into the finite strip method (FSM), and the governing equations are derived based on the first-order shear deformation theory (FSDT). As a convenient approach, boundary conditions are imposed using a simple method based on the RKPM correction function and the essence of the FSDT displacement field. Several examples are studied using this method, and the results are compared to those obtained from other numerical methods. The proposed method is also extended to consider different support geometries and complex inner conditions, and the results are validated using COMSOL finite element software. The shear locking error, which occurs when considering C-0 plate theories, is noticeably reduced by considering the RKPM parameters in the finite strip formulation. (c) 2020 Elsevier Inc. All rights reserved.

关键词： reproducing kernel particle method Static analysis Free vibration Buckling First-order shear deformation Internal support

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Adaptive reproducing kernel particle method using gradient indicator for elasto-plastic deformation

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2013年第2期37卷 280-292页

作者： Liu, H. S. Fu, M. W. Harbin Inst Technol Dept Mechatron Engn Harbin 150001 Peoples R China Hong Kong Polytech Univ Dept Mech Engn Kowloon Hong Kong Peoples R China

An adaptive meshless method based on the multi-scale reproducing kernel particle method (RKPM) for analysis of nonlinear elasto-plastic deformation is proposed in this research. In the proposed method, the equivalent strain, stress, and the second invariant of the Cauchy-Green deformation tensor are decomposed into two scale components, viz., high- and low-scale components by deriving them from the multi-scale decomposed displacement. Through combining the high-scale components of strain and the stress update algorithm, the equivalent stress is decomposed into two scale components. An adaptive algorithm is proposed to locate the high gradient region and enrich the nodes in the region to improve the computational accuracy of RKPM. Using the algorithm, the high-scale components of strain and stress and the second invariant of the Cauchy-Green deformation tensor are normalized and used as criteria to implement the adaptive analysis. To verify the validity of the proposed adaptive meshless method in nonlinear elasto-plastic deformation, four case studies are calculated by the multi-scale RKPM. The patch test results show that the used multi-scale RKPM is reliable in analysis of the regular and irregular nodal distribution. The results of other three cases show that the proposed adaptive algorithm can not only locate the high gradient region well, but also improve the computational accuracy in analysis of the nonlinear elasto-plastic deformation. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Adaptive analysis Multi-scale reproducing kernel particle method High gradient Elasto-plastic deformation

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Application of reproducing kernel particle method and element-free Galerkin method on the simulation of the membrane of capacitive micromachined microphone in viscothermal air

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COMPUTATIONAL MECHANICS 2013年第3期51卷 295-308页

作者： Yang, Cheng-Ta Natl Kaohsiung Marine Univ Dept Marine Engn Kaohsiung 805 Taiwan

Simulation of the microphone membrane determines whether highest yield and sensitivity is attainable when it comes to the field of microelectromechanical system (MEMS) capacitive microphone design. Consequently, it is significantly critical to predict and understand the behavior of the membrane in the air. The reproducing kernel particle method and element-free Galerkin, RKPM and EFG respectively, are introduced to differentiate from the traditional finite element method (FEM) since RKPM and EFG models are meshless to greatly improve the problems of FEM with large size aspect ratio. The result from a numerical axisymmetry model of 1 mm radius and 10 mu m thickness membrane with fixed boundary condition upon 1 mm thickness viscothermal air is identical to that from the theoretical model. Finally, a MEMS axisymmetry model of a 180 mu m radius and 10 mu m thickness membrane upon 10 mu m thickness viscothermal air is simulated in this paper.

关键词： reproducing kernel particle method Element-free Galerkin Capacitive microphone

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The analysis of geometrically nonlinear behavior of SMAs using RKPM

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2025年 142卷

作者： Zhang, Yijie Wei, Gaofeng Liu, Tengda Hua, Fengfeng Zhou, Shasha Qilu Univ Technol Shandong Acad Sci Sch Mech Engn Jinan 250353 Shandong Peoples R China Shandong Inst Mech Design & Res Jinan 250353 Shandong Peoples R China SDEE Hitachi High Voltage Switchgear Co Ltd Jinan Peoples R China

As the temperature surpasses the threshold for the completion of austenitic transformation, shape memory alloys (SMAs) necessitate a substantial external force to trigger internal phase transformation. Given the substantial deformation induced by the external force on SMAs, the application of geometrically nonlinear analysis becomes essential. In this paper, reproducing kernel particle method (RKPM) is employed to investigate the geometrically nonlinear behavior of SMAs. The penalty function method is applied to impose the displacement boundary conditions. The study utilizes the Galerkin weak form with total Lagrangian (TL) framework to develop geometrically nonlinear SMAs equations, solved via Newton-Raphson (N-R) iteration. The effects of varying penalty factor and radius control parameter of the influence domain on error and computational stability are investigated. Ultimately, the suitability of applying RKPM for exploring the geometrically nonlinearity behavior of SMAs is demonstrated via numerical examples.

关键词： Phase transformation Shape memory alloys Geometrically nonlinear behavior reproducing kernel particle method Numerical analysis

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An efficient numerical method for the distributed-order time-fractional diffusion equation with the error analysis and stability properties

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MATHEMATICAL methodS IN THE APPLIED SCIENCES 2025年第3期48卷 2743-2765页

作者： Irandoust-Pakchin, Safar Hossein Derakhshan, Mohammad Rezapour, Shahram Adel, Mohamed Univ Tabriz Fac Math Stat & Comp Sci Dept Appl Math Tabriz Iran Apadana Inst Higher Educ Dept Ind Engn Shiraz Iran Azarbaijan Shahid Madani Univ Dept Math Tabriz Iran Insurance Res Ctr IRC Tehran Iran China Med Univ China Med Univ Hosp Dept Med Res Taichung Taiwan Islamic Univ Madinah Fac Sci Dept Math Medina Saudi Arabia

In this manuscript, we study and examine the time-fractional modified anomalous sub-diffusion model of distributed-order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second-order difference method based on the L1 formula for the temporal variable. In this case, stability and convergence analysis for time discretization using the L1 formula is displayed. For the second approach, we display and demonstrate the numerical method for the full-discrete based on the Galerkin weak form based on various kernels and shape functions of reproducing kernel particle method which do not have the delta$$ \delta $$-Kronecker property. Moreover, in this manuscript, in order to be able to use the necessary boundary conditions, the two straight strategies are used: one is the Lagrange multiplier method, and the other one is the penalty method. By using penalty method, we can the main boundary value model is changed to a new BVP with Robin boundary condition. At the end of the article, some numerical examples are presented and analyzed for the efficiency of the proposed numerical method. Also, the presented numerical method is compared with other numerical approaches, and the results of this comparison are reported in the form of a table.

关键词： distributed-order meshless Galerkin method reproducing kernel particle method stability and convergence time-fractional sub-diffusion model

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A stable meshfree method for simulations of munition penetration into earth

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ENGINEERING WITH COMPUTERS 2024年 1-26页

作者： Atif, Mohammed Mujtaba Chi, Sheng-Wei Li, Xuejun Tian, Jianfei Univ Illinois Chicago IL 60607 USA Ansys Inc Canonsburg PA USA

Meshfree methods, such as the reproducing kernel particle method, have been proven advantageous in modeling excessive deformation problems involving material separation, fracture, impact, etc. However, the domain integration in RKPM remains challenging due to instability and sub-optimal convergence for high strain rate events. Although some novel developments alleviate the above issue, they are either computationally expensive or require evaluating the contour integral, which is not straightforward to obtain in contact and material separation problems using meshfree discretization. This work develops a simple and stable integration method based on the extension of modified Simpson's rule. The method is free from conforming subdomains and can straightforwardly be applied to the meshfree formulation with updated configuration. To model penetration into the earth, a standard viscous boundary is introduced to address the issue of reflecting waves from the truncated computational domain for the ground target. The numerical results are validated with experimental data for various geo-materials and experimental setups.

关键词： reproducing kernel particle method Penetration Soil-structure interaction Domain integration

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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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