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Vibrations of double-nanotube systems with mislocation via a newly developed van der Waals model

PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES 2015年 70卷 58-76页

作者： Kiani, Keivan KN Toosi Univ Technol Dept Civil Engn Tehran Iran

This study deals with transverse vibrations of two adjacent-parallel-mislocatecl single-walled carbon nanotubes (SWCNTs) under various end conditions. These tubes interact with each other and their surrounding medium through the intertube van cler Waals (vdW) forces, and existing bonds between their atoms and those of the elastic medium. The elastic energy of such forces due to the deflections of nanotubes is appropriately modeled by defining a vdW force density function. In the previous works, vdW forces between two identical tubes were idealized by a uniform form of this function. The newly introduced function enables us to investigate the influences of both intertube free distance and longitudinal mislocation on the natural transverse frequencies of the nanosystem which consists of two dissimilar tubes. Such crucial issues have not been addressed yet, even for simply supported tubes. Using nonlocal Timoshenko and higher-order beam theories as well as Hamilton's principle, the strong form of the equations of motion is established. Seeking for an explicit solution to these integro-partial differential equations is a very problematic task. Thereby, an energy-based method in conjunction with an efficient meshfree method is proposed and the nonlocal frequencies of the elastically embedded nanosystem are determined. For simply supported nanosystems, the predicted first five frequencies of the proposed model are checked with those of assumed mode method, and a reasonably good agreement is achieved. Through various studies, the roles of the tube's length ratio, intertube free space, mislocation, small-scale effect, slenderness ratio, radius of SWCNTs, and elastic constants of the elastic matrix on the natural frequencies of the nanosystem with various end conditions are explained. The limitations of the nonlocal Timoshenko beam theory are also addressed. This work can be considered as a vital step towards better realizing of a more complex system that consists of vertica

关键词： Transverse vibration Doubly parallel single-walled carbon nanotubes Van der Waals force reproducing kernel particle method Nonlocal shear deformable beams Mislocation effect

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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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Development of parallel 3D RKPM meshless bulk forming simulation system

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ADVANCES IN ENGINEERING SOFTWARE 2007年第2期38卷 87-101页

作者： Wang, H. Li, Guangyao Han, X. Zhong, Zhi Hua Hunan Univ Coll Mech & Automot Engn State Key Lab Adv Technol Vehicle Design & Manufa Changsha Peoples R China

A parallel computational implementation of modern meshless system is presented for explicit for 3D bulk forming simulation problems. The system is implemented by reproducing kernel particle method. Aspects of a coarse grain parallel paradigm-domain decompose method-are detailed for a Lagrangian formulation using model partitioning. Integration cells are uniquely assigned on each process element and particles are overlap in boundary zones. Partitioning scheme multilevel recursive spectrum bisection approach is applied. The parallel contact search algorithm is also presented. Explicit message passing interface statements are used for all communication among partitions on different processors. The parallel 3D system is developed and implemented into 3D bulk metal forming problems, and the simulation results demonstrated the efficiency of the developed parallel reproducing kernel particle method system. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： parallel reproducing kernel particle method bulk forming domain decomposition method partition message passing interface speedup

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A DAMAGE particle method FOR SMEARED MODELING OF BRITTLE FRACTURE

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INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING 2018年第4期16卷 303-324页

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

Numerical procedures for brittle fracture modeling become tedious when many moving strong discontinuities have to be captured. A smeared fracture modeling approach formulated under the reproducing kernel particle discretization is presented. In this approach, the smeared strain is computed by the divergence operation with a boundary integral of displacements in each nodal representative domain, thus avoiding direct derivatives of displacements for strain computation in the smeared cracking region. To avoid discretization size sensitivity issues, a scaling law is introduced based on the equivalence between the bulk damage energy dissipation and the surface fracture energy of the associated crack segment over the nodal representative domain. This scaling law is introduced under the stabilized conforming nodal integration framework, where the nodal representative domain serves as the smearing domain, and the smeared strain over the nodal representative domain is used with the scaled damage law to determine the damage state. The employment of stabilized conforming nodal integration also allows the displacement and damage state variables to be calculated and stored for the same set of particles, avoiding interpolation of variables between nodal and Gaussian points in conventional finite elements. Several numerical examples are presented to examine the effectiveness of the proposed damage particle method for smeared modeling of fracture.

关键词： smeared strain stabilized conforming nodal integration reproducing kernel particle method smeared crack model continuum damage model

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

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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 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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Efficient searching in meshfree methods

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COMPUTATIONAL MECHANICS 2018年第6期62卷 1461-1483页

作者： Olliff, James Alford, Brad Simkins, Daniel C., Jr. Univ S Florida Dept Civil & Environm Engn 4202 E Fowler Ave ENB118 Tampa FL 33620 USA

Meshfree methods such as the reproducing kernel particle method and the Element Free Galerkin method have proven to be excellent choices for problems involving complex geometry, evolving topology, and large deformation, owing to their ability to model the problem domain without the constraints imposed on the Finite Element method (FEM) meshes. However, meshfree methods have an added computational cost over FEM that come from at least two sources: increased cost of shape function evaluation and the determination of adjacency or connectivity. The focus of this paper is to formally address the types of adjacency information that arises in various uses of meshfree methods;a discussion of available techniques for computing the various adjacency graphs;propose a new search algorithm and data structure;and finally compare the memory and run time performance of the methods.

关键词： Meshfree reproducing kernel particle method Acceleration data structure Nearest neighbour Adjacency Connectivity

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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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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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Penetration modeling of ultra-high performance concrete using multiscale meshfree methods

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL methodS IN GEOMECHANICS 2019年第14期43卷 2328-2351页

作者： Sparks, Paul A. Sherburn, Jesse A. Heard, William F. Williams, Brett A. US Army Engineer Res & Dev Ctr Vicksburg MS USA

Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra-high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it will run inside the reproducing kernel particle method (RKPM)-based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and lastly projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. To ensure arbitrary mesh geometry for which the homogenized stress-strain curves are derived, a size scaling law is incorporated into the homogenized tensile damage evolution law. This ensures energy-bridging equivalence of the microscopic cell to the homogenized medium irrespective of arbitrary mesh geometry. Results of numerical investigations will be compared with results of penetration experiments.

关键词： constitutive modeling multiscale modeling penetration modeling reproducing kernel particle method ultra-high performance concrete

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