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Analysis of laminated composite plates based on THB-RKPM method using the higher-order shear deformation plate theory

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SCIENTIA IRANICA 2019年第4期26卷 2057-2078页

作者： Atri, H. R. Shojaee, S. Shahid Bahonar Univ Kerman Dept Civil Engn Kerman Iran

In the present investigation, static free vibration and buckling response of laminated composite plates based on coupling of Truncated Hierarchical B-splines (THBsplines) with reproducing kernel particle method (RKPM) through higher-order shear deformation plate theory are presented. The coupled THB-RKPM method blends the advantages of the isogeometric analysis and meshfree methods. Since under certain conditions, the isogeometric B-spline and NURBS basis functions are exactly represented by reproducing kernel meshfree shape functions, recursive process of producing isogeometric bases can be omitted. More importantly, a seamless link between meshfree methods and isogeometric analysis can easily be defined, which provides an authentic meshfree approach to refining the model locally in isogeometric analysis. This procedure can be carried out using truncated hierarchical B-splines to construct new bases and adaptively refine them. It is shown that the THEt-RKPM method is ideally appropriate for local refinement of laminated composite plates in the framework of isogeometric analysis. The flexibility of the proposed method for refining basis functions leads to decrease in the computational cost without losing the accuracy of the solution. Numerical examples considering different boundary conditions and various aspect ratios, stiffness ratios, and fiber orientations demonstrated validity and versatility of the proposed method. (C) 2019 Sharif University of Technology. All rights reserved.

关键词： Laminated composite plates Higher-order shear deformation theory NURBS THB-splines reproducing kernel particle method

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Meshfree truncated hierarchical refinement for isogeometric analysis

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COMPUTATIONAL MECHANICS 2018年第6期62卷 1583-1597页

作者： Atri, H. R. Shojaee, S. Shahid Bahonar Univ Kerman Dept Civil Engn Kerman Iran

In this paper truncated hierarchical B-spline (THB-spline) is coupled with reproducing kernel particle method (RKPM) to blend advantages of the isogeometric analysis and meshfree methods. Since under certain conditions, the isogeometric B-spline and NURBS basis functions are exactly represented by reproducing kernel meshfree shape functions, recursive process of producing isogeometric bases can be omitted. More importantly, a seamless link between meshfree methods and isogeometric analysis can be easily defined which provide an authentic meshfree approach to refine the model locally in isogeometric analysis. This procedure can be accomplished using truncated hierarchical B-splines to construct new bases and adaptively refine them. It is also shown that the THB-RKPM method can provide efficient approximation schemes for numerical simulations and represent a promising performance in adaptive refinement of partial differential equations via isogeometric analysis. The proposed approach for adaptive locally refinement is presented in detail and its effectiveness is investigated through well-known benchmark examples.

关键词： Truncated hierarchical B-spline Meshfree reproducing kernel particle method NURBS Refinement

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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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A combined meshfree/finite strip method for analysis of plates with perforations and cracks

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THIN-WALLED STRUCTURES 2017年第Feb.期111卷 113-125页

作者： Khezri, M. Abbasi, M. Rasmussen, K. J. R. Univ Sydney Sch Civil Engn Sydney NSW 2006 Australia

This work presents a coupling of the finite strip method (FSM) and the meshless reproducing kernel particle method (RKPM), which is inspired by the complementary features of both methods. A straightforward and effective method is developed to accurately integrate these methods, and the obtained coupled technique is utilised for analysing two-dimensional linear elastic plates weakened by arbitrarily shaped perforations or cracks. The RKPM is used in the regions surrounding the cracks, i.e. parts of the domain with high gradients and irregular boundaries, whereas the FSM is adopted in the rest of the domain. The sub-domains of these methods are conjoined over transition zones by utilising a modified collocation approach which ensures the linear consistency of the approximation field. A series of numerical examples and studies of the obtained convergence rates are presented to demonstrate the accuracy and effectiveness of the developed coupled method.

关键词： Finite strip method Meshless reproducing kernel particle method Combined method Perforated plates

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The complex variable reproducing kernel particle method for two-dimensional elastodynamics

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Chinese Physics B 2010年第9期19卷 59-70页

作者：陈丽程玉民 Department of Engineering Mechanics Chang'an University Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.

关键词： meshless method reproducing kernel particle method complex variable reproducing kernel particle method elastodvnamics

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Simulation of sheet metal forming process using reproducing kernel particle method

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN BIOMEDICAL ENGINEERING 2010年第11期26卷 1462-1476页

作者： Liu, H. S. Xing, Z. W. Yang, Y. Y. Harbin Inst Technol Sch Mechatron Engn Harbin 150006 Peoples R China Harbin Inst Technol Sch Mat Sci & Engn Harbin 150006 Peoples R China

Numerical simulation of sheet metal forming process using the meshless method called reproducing kernel particle method (RKPM) is studied in this paper. Owing to limitations of meshless approximation under parametric coordinate system, a constrained reproducing kernel (RK) approximation under Cartesian coordinate system is employed to describe the sheet metal deformation. Several technologies are used to solve the crucial problems involved in the numerical procedure. RKPM shape function is modified to impose essential boundary conditions;stabilized conforming nodal integration method is adopted to implement numerical integration of weak formulation;and an algorithm based on moment method is used to treat contact detection during sheet metal forming process. A program based on constrained RK approximation is developed to simulate two sheet metal forming examples: square-cup deep drawing and hemispherical part drawing. Numerical results are presented to demonstrate the effectiveness of the RKPM in numerical simulation of sheet metal forming. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： meshless methods reproducing kernel particle method sheet metal forming essential boundary condition reproducing kernel approximation

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Meshfree and finite element modelling of impact: A comparative study

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INTERNATIONAL JOURNAL OF IMPACT ENGINEERING 2016年第Apr.期90卷 146-153页

作者： Kumar, V. Ramamurthy, K. Univ Madras Dept Comp Sci Madras 600113 Tamil Nadu India

Many methods have been developed in order to study the impact behaviour of solids and structures. Two common methods are meshfree method and the finite element method. The smoothed finite element method has become a powerful alternative to the finite element method as it promises to model large deformations and high mesh distortion without much loss of accuracy. In this manuscript, we present a comparative study of the finite element method, the smoothed finite element method and nodal stabilised reproducing kernel particle method with respect to their ability to predict impact events. The same constitutive models are applied for all computational methods. Through numerical examples, we show that meshfree methods can predict impact events most accurately but they are also computational more costly. We also show that the smoothed finite element method does not yield in an improvement compared to the finite element method. All results are compared to experimental data. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Impact Meshfree method reproducing kernel particle method Smoothed finite element method

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Surface and shear energy effects on vibrations magnetically affected beam-like nanostructures carrying direct currents

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2016年 113卷 221-238页

作者： Kiani, Keivan KN Toosi Univ Technol Dept Civil Engn POB 15875-4416Valiasr Ave Tehran Iran

Free vibration of current-carrying nano-scaled beams immersed in a magnetic field is of huge interest. To bridge this scientific gap, Rayleigh, Timoshenko, and higher-order beam models accounting for the surface energy are employed and their equations of motion are established appropriately. For spatial discretization of the deformations fields, a meshless approach is exploited. The effects of surface and shear deformation, electric current, magnetic field strength, and geometric parameters of the nanobeam on the first ten natural frequencies are examined and discussed. The critical values of slenderness ratio, nanobeam's diameter, electric current, and magnetic field strength, which are corresponding to the dynamically unstable nanobeams, are graphically identified. The obtained results indicate that the discrepancies between the frequencies by considering the surface effect and those evaluated without consideration of the surface energy would increase notably at the above-mentioned critical values. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Nanobeams Transverse vibrations Direct electric current Surface energy effect Shear deformable beam theories reproducing kernel particle method

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A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media

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COMPUTERS & FLUIDS 2016年 141卷 105-115页

作者： Wei, Haoyan Chen, Jiun-Shyan Hillman, Michael Univ Calif San Diego Dept Struct Engn 9500 Gilman Dr La Jolla CA 92093 USA

Numerical modeling of reservoirs with low permeability or under undrained conditions often suffers from spurious fluid pressure oscillations due to the improper construction of approximation spaces. To address this issue, a fully coupled, stabilized meshfree formulation is developed based on a fluid pressure projection method, in which an additional stabilization term is added to the variational equation to correct the deficiency of the equal-order u-p reproducing kernel approximation. The projection scheme is formulated under the framework of the stabilized conforming nodal integration which enables a significant enhancement of the computational efficiency and accuracy, and the spurious low-energy modes of nodal integration are also eliminated. The effectiveness of the proposed stabilized meshfree formulation is demonstrated by solving several benchmark problems. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Meshfree methods reproducing kernel particle method Stabilized conforming nodal integration Pressure projection Fluid-saturated porous media Coupled hydro-mechanical analysis

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An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2016年第7期107卷 603-630页

作者： Hillman, Michael Chen, Jiun-Shyan Univ Calif San Diego Dept Struct Engn 9500 Gilman Dr San Diego CA 92093 USA

Convergent and stable domain integration that is also computationally efficient remains a challenge for Galerkin meshfree methods. High order quadrature can achieve stability and optimal convergence, but it is prohibitively expensive for practical use. On the other hand, low order quadrature consumes much less CPU but can yield non-convergent, unstable solutions. In this work, an accelerated, convergent, and stable nodal integration is developed for the reproducing kernel particle method. A stabilization scheme for nodal integration is proposed based on implicit gradients of the strains at the nodes that offers a computational cost similar to direct nodal integration. The method is also formulated in a variationally consistent manner, so that optimal convergence is achieved. A significant efficiency enhancement over a comparable stable and convergent nodal integration scheme is demonstrated in a complexity analysis and in CPU time studies. A stability analysis is also given, and several examples are provided to demonstrate the effectiveness of the proposed method for both linear and nonlinear problems. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： nodal integration reproducing kernel particle method stabilization variational consistency implicit gradient

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