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Meshfree digital image correlation using reproducing kernel particle method and its degenerate derivations

MEASUREMENT 2024年 226卷

作者： Chen, Bin Coppieters, Sam KTH Royal Inst Technol Wallenberg Wood Sci Ctr Dept Fiber & Polymer Technol SE-10044 Stockholm Sweden Katholieke Univ Leuven Dept Mat Engn Ghent CampusGebroeders De Smetstr 1 B-9000 Ghent Belgium

Meshfree digital image correlation (MF-DIC) is a recently-proposed advanced DIC technique that deeply integrates meshfree method with DIC. MF-DIC is of potential due to its close relationship with computational mechanics and the excellent balance between spatial resolution and measurement resolution. A new MF-DIC algorithm based on another advanced meshfree method, namely the reproducing kernel particle method (RKPM), is proposed. The RKPM-based MF-DIC is proven to be equivalent to the recently-proposed Element Free Galerkin method (EFGM) based MF-DIC in certain conditions. This work also briefly introduces two additional MF-DIC methods based on smooth particle hydrodynamics (SPH) and the point interpolation method (PIM). In certain cases, they are the degenerative derivations of the RKPM-based MF-DIC. Benchmark tests on DIC Challenge 2.0 show that these MF-DIC methods also have a superior balance between spatial resolution and measurement resolution compared to state-of-the-art DIC algorithms.

关键词： Meshfree digital image correlation Reproducing kernel point method Metrological efficiency indicator point interpolation method Smooth particle hydrodynamics

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An efficient adaptive analysis procedure using the edge-based smoothed point interpolation method (ES-PIM) for 2D and 3D problems

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2012年第9期36卷 1424-1443页

作者： Tang, Q. Zhang, G. Y. Liu, G. R. Zhong, Z. H. He, Z. C. Univ Western Australia Sch Mech & Chem Engn Nedlands WA 6009 Australia Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Natl Univ Singapore Dept Mech Engn Singapore 117576 Singapore Univ Cincinnati Sch Aerosp Syst Cincinnati OH 45221 USA

In this paper, an efficient adaptive analysis procedure is proposed using the newly developed edge-based smoothed point interpolation method (ES-PIM) for both two dimensional (2D) and three dimensional (3D) elasticity problems. The ES-PIM works well with three-node triangular and four-node tetrahedral meshes, is easy to be implemented for complicated geometry, and can obtain numerical results of much better accuracy and higher convergence rate than the standard finite element method (FEM) with the same set of meshes. All these important features make it an ideal candidate for adaptive analysis. In the present adaptive procedure, a novel error indicator is devised for ES-PIM settings, which evaluates the maximum difference of strain energy values among the vertexes of each background cell. A simple h-type local refinement scheme is adopted together with a mesh generator based on Delaunay technology. Intensive numerical studies of 20 and 3D examples indicate that the proposed adaptive procedure can effectively capture the stress concentration and solution singularities, carry out local refinement automatically, and hence achieve much higher convergence for the solutions in strain energy norm compared to the general uniform refinement. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Meshfree methods Error indicator Adaptive analysis point interpolation method Delaunay triangulation

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A strain-constructed point interpolation method and strain field construction schemes for solid mechanics problems using triangular mesh

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APPLIED MATHEMATICS AND COMPUTATION 2012年第4期219卷 2067-2086页

作者： Zhang, G. Y. Liu, G. R. Xu, X. Univ Western Australia Sch Mech & Chem Engn Intelligent Syst Med Lab Perth WA 6009 Australia Univ Cincinnati Sch Aerosp Syst Cincinnati OH 45221 USA Jilin Univ Coll Math Changchun 130012 Peoples R China

This paper presents a strain-constructed point interpolation method (SC-PIM) for solid mechanics problems using three-node triangular mesh. In the SC-PIM, the point interpolation method (PIM) is used to construct both displacement and strain fields. A total of 14 schemes are proposed to construct strain fields that are equivalent to the compatible strain fields in energy norm, and therefore the strain-constructed Galerkin (SC-Galerkin) weak form can be used to form the discretized system equations. In these schemes, strains at critical points (vertices of the triangular integration cells) are first obtained using the generalized strain smoothing techniques over the node-based and/or edge-based smoothing domains, and constructed strain fields in the integration cells are then obtained using linear interpolations. A SC-PIM model using any of the 14 schemes is stable and convergent, but not necessarily to the exact solution. Standard numerical patch tests are conducted to find six linearly conforming schemes converging to the exact solution. Benchmark problems have been studied to investigate the performance and properties of the SC-PIM with all these six conforming schemes. Outstanding schemes have been identified with better accuracy and high convergence rates in terms of both displacement and energy norms. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Numerical methods Meshfree methods point interpolation method Strain construction Gradient smoothing

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Response of a Layered Composite Beam Subjected to Static Loading Using point interpolation Meshless Technique 2nd

Response of a Layered Composite Beam Subjected to Static Loa...

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2nd International Conference on Mechanical Engineering Design,ICMechD 2019

作者： Shah, Kunal S. Gadade, Appaso M. Sansgiri, Sanjiv M. Mechanical Engineering Army Institute of Technology Pune411015 India Mechanical Engineering Department Thapar Institute of Engineering and Technology Patiala147004 India

ISBN: (纸本)9789811544873

The present work proposes a meshless model to analyze the response of laminated composite beam under different types of static loading. The point interpolation method based on polynomial basis function is used for solving 1D higher-order beam theory equations. The distribution of transverse shear strain and stresses along thickness are obtained using Reddy’s shape function. A displacement response of a laminated beam is obtained for several lamination schemes, aspect ratio, and boundary conditions. The authenticity of the present algorithm is confirmed by comparing results with different cases from literature. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Higher-order beam theory Laminated composite beam Meshless method point interpolation method

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The Nonconforming point interpolation method Applied to Electromagnetic Problems

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IEEE TRANSACTIONS ON MAGNETICS 2012年第2期48卷 619-622页

作者： Lima, Naisses Z. Mesquita, Renato C. Facco, Werley G. Moura, Alex S. Silva, Elson J. Univ Fed Minas Gerais Grad Program Elect Engn BR-31270010 Belo Horizonte MG Brazil Univ Fed Minas Gerais Dept Elect Engn BR-31270010 Belo Horizonte MG Brazil Fed Univ Vales Jequitinhonha & Mucuri Dept Exact Sci BR-39803371 Diamantina MG Brazil

Nonconforming point interpolation method (NPIM) is a meshless method that has been applied to problems in mechanics in the last years. In this paper, we investigate NPIM in electromagnetism. We present its formulation and shape functions, which are generated by the radial point interpolation method with polynomial terms. The numerical results are compared to the ones obtained by the finite flement method (FEM) and the element-free Galerkin method (EFG).

关键词： Element-free Galerkin (EFG) finite element method meshless point interpolation method

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A novel PIM-based triangular element and its validations

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CONTINUUM MECHANICS AND THERMODYNAMICS 2020年第1期32卷 75-98页

作者： Huang, Zhecong Xue, Xinhua Sichuan Univ Coll Water Resource & Hydropower 24 South Sect 1Yihuan Rd Chengdu 610065 Peoples R China

Using the point interpolation method, this study proposes a distinctive node selection scheme, T33-scheme, to construct the approximation over all triangles in the mesh. By the T33-scheme, we always selects out six nodes to take part in the interpolation to any element, creating a T33 element with a displacement approximation of completely quadratic polynomials. The six nodes may be real nodes in the mesh or assistant nodes temporarily generated during the calculation of the element matrices. The degrees of freedom of assistant nodes can be easily condensed off once the matrices of the element, which has one boundary edge, are formed. The T33 element can pass the patch test exactly and reproduce the displacement mode of quadratic polynomials. Numerical experiments confirmed that the T33 elements have an outstanding performance in its accuracy, convergence rates and stability.

关键词： point interpolation method T33 element Meshless Quadratic polynomials

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APPLICATION OF point interpolation method IN JOINTED ROCK MASS

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2011年第1期8卷 41-55页

作者： Hajiazizi, M. Ashory, M. R. Semnan Univ Dept Civil Engn Semnan Iran Semnan Univ Sch Mech Engn Semnan Iran

In this paper, point interpolation method (PIM) is applied to analyze the nonlinear and elastoplastic behavior of jointed rock masses. PIM is advantageous over the other meshless methods that are based on moving least square (MLS) technique. On the other hand in this study, element-free Galerkin method (EFGM) has been applied to analyze a jointed rock mass for comparison purposes. The domain of jointed rock mass is represented by a set of arbitrary distributed nodes. The essential boundary conditions are imposed in EFGM using penalty method. Mohr-Coulomb failure criterion is used for analyzing the behavior of joint failure. Two numerical examples are considered to demonstrate the effectiveness of method in predicting the elastoplastic behavior of jointed rock mass. The results are compared with those of finite difference method (FDM).

关键词： point interpolation method elastoplastic analysis jointed rock mass

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A CONFORMING point interpolation method (CPIM) BY SHAPE FUNCTION RECONSTRUCTION FOR ELASTICITY PROBLEMS

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2010年第3期7卷 369-395页

作者： Xu, X. Liu, G. R. Gu, Y. T. Zhang, G. Y. Jilin Univ Coll Math Changchun 130021 Peoples R China Singapore MIT Alliance SMA Singapore 117576 Singapore Queensland Univ Technol Sch Engn Syst Brisbane Qld 4001 Australia Natl Univ Singapore Ctr Adv Computat Engn Sci ACES Dept Mech Engn Singapore 117576 Singapore

A conforming point interpolation method (CPIM) is proposed based on the Galerkin formulation for 2D mechanics problems using triangular background cells. A technique for reconstructing the PIM shape functions is proposed to create a continuous displacement field over the whole problem domain, which guarantees the CPIM passing the standard patch test. We prove theoretically the existence and uniqueness of the CPIM solution, and conduct detailed analyses on the convergence rate;computational efficiency and band width of the stiffness matrix of CPIM. The CPIM does not introduce any additional degrees of freedoms compared to the linear FEM and original PIM;while convergence rate of quadratic CPIM is in between that of linear FEM and quadratic FEM which results in the high computational efficiency. Intensive numerical studies verify the properties of the CPIM.

关键词： Numerical method computational method finite element method meshfree methods point interpolation method convergence rates, computational efficiency, non-conforming

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An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2010年第9-10期53卷 1938-1950页

作者： Wu, S. C. Liu, G. R. Cui, X. Y. Nguyen, T. T. Zhang, G. Y. Hefei Univ Technol Sch Mat Sci & Engn Ctr Adv Mat Joining & Simulat AMJS Hefei 230009 Peoples R China Natl Univ Singapore Dept Mech Engn Ctr Adv Computat Engn Sci ACES Singapore 117576 Singapore Singapore MIT Alliance SMA Singapore 117576 Singapore Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for analyzing 2D and 3D transient heat transfer problems with mixed boundary conditions and complicated geometries. In the ES-PIM, shape functions are constructed using the polynomial PIM with the Delta function property for easy treatment of essential boundary conditions A generalized smoothing technique is used to reconstruct the temperature gradient field within the edge-based smoothing domains. The generalized smoothed Galerkin weak form is then used to establish the discretized system equations. Our results show that the ES-PIM can provide more close-to-exact stiffness compared with the "overly-stiff" finite element method (FEM) and the "overly-soft" node-based smoothed point interpolation method (NS-PIM). Owing to this important property, the present ES-PIM provides more accurate solutions than standard FEM using the same mesh. As an example, a practical cooling system of the rapid direct plasma deposition dieless manufacturing is studied in detail using the present ES-PIM, and a set of "optional" processing parameters of fluid velocity and temperature are found. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Numerical methods Meshfree method Transient heat transfer Gradient smoothing point interpolation method Rapid plasma deposition dieless manufacturing

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A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2010年第10期46卷 862-874页

作者： Xu, X. Liu, G. R. Gu, Y. T. Zhang, G. Y. Luo, J. W. Peng, J. X. Jilin Univ Coll Math Changchun 130012 Peoples R China Singapore MIT Alliance SMA Singapore 117576 Singapore Queensland Univ Technol Sch Engn Syst Brisbane Qld 4001 Australia Natl Univ Singapore Dept Mech Engn Ctr Adv Computat Engn Sci ACES Singapore 117576 Singapore

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM-LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very "tight'' lower and upper bound solutions can be obtained using PIM-LS2. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Finite element method Meshfree methods point interpolation method Solution bounds Extended Galerkin Softening effect

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