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Meshfree method for 3D bulk forming analysis with lower order integration scheme

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2004年第10期28卷 1283-1292页

作者： Li, GY Sidibe, K Liu, GR Hunan Univ Coll Mech & Automot Engn Changsha 410082 Hunan Peoples R China

Three-dimensional (3D) bulk forming simulation by reproducing kernel particle method is presented in this paper. For increasing computational efficiency a lower order integration scheme is proposed and a general benchmark test for explicit non-linear program is developed, to verify the correctness and the accuracy of the present scheme. A particle to segment contact algorithm for treatment of the contact between deformable and rigid bodies is also presented. The algorithm is found to be very effective and suitable for 3D bulk forming analysis. (C) 2004 Elsevier Ltd. All fights reserved.

关键词： reproducing kernel particle method reduced integration benchmark test contact bulk forming

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Immersed finite element method and its applications to biological systems

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2006年第13-16期195卷 1722-1749页

作者： Liu, WK Liu, YL Farrell, D Zhang, L Wang, XS Fukui, Y Patankar, N Zhang, YJ Bajaj, C Lee, J Hong, JH Chen, XY Hsu, HY Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Tulane Univ Dept Mech Engn New Orleans LA 70118 USA New Jersey Inst Technol Dept Math Sci Newark NJ 07102 USA Northwestern Univ Feinberg Sch Med Dept Cell & Mol Biol Chicago IL 60611 USA Univ Texas Dept Comp Sci Inst Computat Engn & Sci Austin TX 78712 USA Univ Texas Dept Comp Sci Dept Comp Sci Austin TX 78712 USA Seoul Natl Univ Sch Mech & Aerosp Engn Seoul 151742 South Korea

This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility. (c) 2005 Elsevier B.V. All rights reserved.

关键词： immersed finite element method reproducing kernel particle method fluid-structure interaction cytoskeletal dynamics red blood cell aggregation thrombosis cardiovascular system micro-circulation naiio-electro-mechanical-sensors cell motility surgical corrective procedures

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A reproducing kernel smooth contact formulation for metal forming simulations

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COMPUTATIONAL MECHANICS 2014年第1期54卷 151-169页

作者： Wang, Hui-Ping Wu, Cheng-Tang Chen, Jiun-Shyan GM Global R&D Ctr Warren MI 48090 USA Livermore Software Technol Corp Livermore CA 94550 USA Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA

This paper presents a meshfree smooth contact formulation for application to metal forming problems. The continuum-based contact formulation requires continuity in the approximation of contact surface geometry and displacement variables, which is difficult for the conventional finite elements. In this work, we introduce a reproducing kernel approximation to achieve arbitrary degree of smoothness for contact surface representation and displacement field approximation. This approach allows the employment of continuum-based contact formulation, leading to a continuous contact force vector and a consistent tangent particularly advantageous in the Newton iteration of contact analysis. The proposed meshfree smooth contact formulation has been applied to the simulation of metal forming processes and is shown to improve the convergence significantly in comparison with the finite element-based contact formulation.

关键词： Meshfree method Contact formulation reproducing kernel particle method Smooth contact Metal forming simulation

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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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Microstructural analysis of skeletal muscle force generation during aging

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN BIOMEDICAL ENGINEERING 2020年第1期36卷 e3295-e3295页

作者： Zhang, Yantao Chen, Jiun-Shyan He, Qizhi He, Xiaolong Basava, Ramya R. Hodgson, John Sinha, Usha Sinha, Shantanu Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Univ Calif Los Angeles Dept Integrat Biol & Physiol Los Angeles CA USA San Diego State Univ Dept Phys San Diego CA 92182 USA Univ Calif San Diego Dept Radiol La Jolla CA 92093 USA

Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based reproducing kernel particle method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. Novelty Statement A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using reproducing kernel particle method (RKPM). The employed RKPM offers an effective means for

关键词： aging connective tissue force generation microstructure numerical simulation reproducing kernel particle method skeletal muscle

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Simulation and prediction of endothelial cell adhesion modulated by molecular engineering

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2008年第25-28期197卷 2340-2352页

作者： Kopacz, Adrian Marcin Liu, Wing Kam Liu, Shu Q. Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Northwestern Univ Dept Biomed Engn Evanston IL 60208 USA

Computational modeling is an effective approach for simulating and predicting the development and remodeling of biological systems. Here, we propose to integrate a probabilistic mathematical modeling approach into an emerging bioengineering area known as molecular regenerative engineering. This experimental-computational framework can be used to simulate and predict the efficacy of molecular engineering in controlling and enhancing the regenerative processes of pathologically disordered cells, tissues and organs. We demonstrate the significance and principles of this approach by using a special case as an example: enhancement of endothelial cell adhesion to arterial constructs by siRNA-mediated modulation of an adhesion-inhibiting factor known as Src homology 2 domain-containing protein tyrosine phosphatase (SHP)-1. A continuum approach is used to model endothelial cell adhesion at the cellular level, while the Kramers reaction-rate theory is used to model cell adhesion at the subcellular and molecular levels. We show that the proposed computational model can potentially be used to simulate the processes and alterations of endothelial cell adhesion at the molecular and cellular levels under shear flow and to predict the effectiveness of siRNA-mediated SHP-1 knockdown in enhancing endothelial cell adhesion in arterial constructs. These preliminary investigations suggest that this integrated experimental-computational approach may be used for the simulation and prediction of regenerative processes in response to molecular engineering. (C) 2008 Elsevier B.V. All rights reserved.

关键词： immersed finite element method reproducing kernel particle method mesh-free method fluid-structure interaction endothelial cell adhesion arterial reconstruction atherosclerosis

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Analysis of rectangular laminated composite plates via FSDT meshless method

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2002年第7期44卷 1275-1293页

作者： Wang, J Liew, KM Tan, MJ Rajendran, S Nanyang Technol Univ Sch Mech & Prod Engn Ctr Adv Numer Engn Simulat Singapore 639798 Singapore

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： meshless reproducing kernel particle method RKPM bending free vibration buckling laminated composite plates first-order shear defori-nation plate theory

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Numerical method for shape optimization using meshfree method

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2003年第6期24卷 418-429页

作者： Kim, NH Choi, KK Botkin, ME Univ Florida Dept Mech Engn Gainesville FL 32611 USA Univ Iowa Ctr Comp Aided Design Iowa City IA 52242 USA GM Corp Vehicle Anal & Dynam R&D & Planning Warren MI 48090 USA

A numerical method for continuum-based shape design sensitivity analysis and optimization using the meshfree method is proposed. The reproducing kernel particle method is used for domain discretization in conjunction with the Gauss integration method. Special features of the meshfree method from a sensitivity analysis viewpoint are discussed, including the treatment of essential boundary conditions, and the dependence of the shape function on the design variation. It is shown that the mesh distortion that exists in the finite element-based design approach is effectively resolved for large shape changing design problems through 2-D and 3-D numerical examples. The number of design iterations is reduced because of the accurate sensitivity information.

关键词： design sensitivity analysis shape optimization meshfree method reproducing kernel particle method

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Nonlocal axial load-bearing capacity of two neighboring perpendicular single-walled carbon nanotubes accounting for shear deformation

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PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES 2015年 74卷 270-286页

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

This study is devoted to examine load-bearing capacity of a nanosystem composed of two adjacent perpendicular single-walled carbon nanotubes (SWCNTs) which are embedded in an elastic matrix. Accounting for the nonlocality and the intertube van der Waals forces, the governing equations are established based on the nonlocal Euler-Bernoulli, Timoshenko, and higher-order beam theories. These are sets of coupled integro-ordinary differential equations whose analytical solutions are unavailable. Hence, an efficient meshless methodology is proposed and the discrete governing equations are obtained via Galerkin approach. By solving the resulting set of eigenvalue equations, the axial buckling load of the elastically embedded nanosystem is evaluated. The roles of the radius and slenderness ratio of the constitutive SWCNTs, free distance between two tubes, small-scale parameter, aspect ratio, transverse and rotational stiffness of the surrounding matrix on the axial buckling load of the nanosystem are comprehensively addressed. The obtained results can be regarded as a pivotal step for better understanding the mechanism of elastic buckling of more complex systems such as elastically embedded-orthogonal membranes or even forests of SWCNTs. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Axial buckling behavior Two adjacent single-walled carbon nanotubes Nonlocal beam theories Modeling of van der Waals forces reproducing kernel particle method Assumed mode approach

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Numerical aspects of a real-time sub-structuring technique in structural dynamics

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2007年第11期72卷 1261-1313页

作者： Sajeeb, R. Roy, D. Manohar, C. S. Indian Inst Sci Dept Civil Engn Struct Lab Bangalore 560012 Karnataka India

A time domain coupling technique, involving combined computational and experimental modelling, for vibration analysis of structures built-up of linear/non-linear substructures is developed. The study permits, in principle, one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom. The numerical and experimental substructures are allowed to communicate in real time within the present framework. The proposed strategy involves a two-stage scheme: the first is iterative in nature and is implemented at the initial stages of the solution in a non-real-time format;the second is non-iterative, employs an extrapolation scheme and proceeds in real time. Issues on time delays during communications between different substructures are discussed. An explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions. The stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high-frequency errors is presented. For systems with non-linear substructures, the integration procedure is based on a multi-step transversal linearization method;and, to account for time delays, we employ a multi-step extrapolation scheme based on the reproducing kernel particle method. Numerical illustrations on a few low-dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real-time substructure testing techniques. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： real-time sub-structuring numerical and experimental sub-structures extrapolations reproducing kernel particle method explicit and implicit time-stepping schemes

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