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  • Open Access


    A Frictionless Contact Algorithm for Meshless Methods

    R. Vignjevic1, T. De Vuyst2, J. C. Campbell1

    CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.1, pp. 35-48, 2006, DOI:10.3970/cmes.2006.013.035

    Abstract An approach to the treatment of contact problems involving frictionless sliding and separation under large deformations in meshless methods is proposed. The method is specially suited for non-structured spatial discretisation. The contact conditions are imposed using a contact potential for particles in contact. Inter-penetration is checked as a part of the neighbourhood search. In the case of conventional SPH contact conditions are enforced on the boundary layer 2h thick while in the case of the normalized SPH contact conditions are enforced for the particles lying on the contact surface. The implementation of the penalty based More >

  • Open Access


    Numerical Computation of Discrete Differential Operators on Non-Uniform Grids

    N. Sukumar1, J. E. Bolander1

    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 691-706, 2003, DOI:10.3970/cmes.2003.004.691

    Abstract In this paper, we explore the numerical approximation of discrete differential operators on non-uniform grids. The Voronoi cell and the notion of natural neighbors are used to approximate the Laplacian and the gradient operator on irregular grids. The underlying weight measure used in the numerical computations is the {\em Laplace weight function}, which has been previously adopted in meshless Galerkin methods. We develop a difference approximation for the diffusion operator on irregular grids, and present numerical solutions for the Poisson equation. On regular grids, the discrete Laplacian is shown to reduce to the classical finite More >

  • Open Access


    A MLPG (LBIE) method for solving frequency domain elastic problems

    E. J. Sellountos1, D. Polyzos2

    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 619-636, 2003, DOI:10.3970/cmes.2003.004.619

    Abstract A new meshless local Petrov-Galerkin (MLPG) method for solving two dimensional frequency domain elastodynamic problems is proposed. Since the method utilizes, in its weak formulation, either the elastostatic or the frequency domain elastodynamic fundamental solution as test function, it is equivalent to the local boundary integral equation (LBIE) method. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and boundary variables is employed. Two integral equations suitable for the integral representation of the displacement fields in the local sub- domains are… More >

  • Open Access


    A New Interface Identification Technique Based on Absolute Density Gradient for Violent Flows

    Yan Zhou1, Qingwei Ma*

    CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.2, pp. 131-147, 2018, DOI: 10.3970/cmes.2018.00249

    Abstract An identification technique for sharp interface and penetrated isolated particles is developed for simulating two-dimensional, incompressible and immiscible two-phase flows using meshless particle methods in this paper. This technique is based on the numerically computed density gradient of fluid particles and is suitable for capturing large interface deformation and even topological changes such as merging and breaking up of phases. A number of assumed particle configurations will be examined using the technique, including these with different level of randomness of particle distribution. The tests will show that the new technique can correctly identify almost all More >

  • Open Access


    Meshless method for solving a free boundary problem associated with obstacle

    DaMing Yuan, XiaoLiang Cheng

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.17, No.2, pp. 53-54, 2011, DOI:10.3970/icces.2011.017.053

    Abstract In this paper, we discuss the numerical method for solving the i??rst kind of elliptic variational inequality. We i??rst use the fundamental solution as the basis function to approximate the solution of variational inequality, then we employ the Uzawa's algorithm to determine the free boundary and the solution. Numerical examples are given to testify the efi??ciency of the method. More >

  • Open Access


    Modelling 3D rock slope with a single elliptic joint surface by a meshless method

    Xiaoying Zhuang, Yongchang Cai, Hehua Zhu.

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.20, No.3, pp. 81-82, 2011, DOI:10.3970/icces.2011.020.081

    Abstract Meshless methods have shown advantages in dealing with problems of moving interfaces such as crack propagation in rock. In Tongji University, meshless methods, the meshless Shepard and least squares (MSLS) method and the element-free Galerkin (EFG) method have been applied to slope stability analysis, especially for rock slope stability governed by a number of dominating discontinuities. Previous studies have focused on 2D problems where a joint surface is modelled as a crack line [1]. In this paper, the EFG method is extended for analyzing 3D rock slope with a single planner elliptic joint. Due to More >

  • Open Access


    A New Combined Scheme of Discrete Element Method and Meshless Method for Numerical Simulation of Impact Problems

    Li Shan, Ming Cheng, Kaixin Liu

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.3, pp. 87-88, 2011, DOI:10.3970/icces.2011.019.087

    Abstract In the present paper, a combined scheme of discrete element method (DEM) and meshless method for numerical simulation of impact problems is proposed. Based on the basic principle of continuum mechanics, an axisymmetric DEM framework is estabilished for modeling the elastoplastic behavior of solid materials. A failure criterion is introduced to model the transformation from a continuum to a discontinuum. The friction force between contact elements is also considered after the failure appears. So our scheme can calculate not only the behavior of continuum and discontinuum, but also the transformation process from continuum to discontinuum. More >

  • Open Access


    The Progress of Energy Meshless Methods by Using Trial Functions as the Bases of Solution

    Cheinshan Liu1,2,3, Chunglun Kuo2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 189-191, 2019, DOI:10.32604/icces.2019.05074

    Abstract For the linear differential operator equation equipped with boundary conditions we derive an energy identity. Then we propose an energy regularization technique to choose the energetic bases in the numerical solution of linear differential operator equation. In many meshless methods with some trial functions as the bases of numerical solution, there exist certain parameters in the numerical method. We derive a very simple energy gap functional and minimize it to determine the optimal parameters. The new methodology upon adopting optimal parameters by minimizing the energy gap functional can improve the accuracy of the meshless methods More >

  • Open Access


    Meshless Methods in Computational Biomechanics for Medicine

    Karol Miller

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 188-188, 2019, DOI:10.32604/icces.2019.06116

    Abstract The field of Biomechanics is in the most exiting state of transition from the theoretical subject of the 20th century to a practical discipline providing patient-specific solutions in the 21st century. Computational biomechanics is becoming instrumental in enabling a new era of personalized medicine based on patient-specific scientific computations. The Finite Element Method is used by almost all members of computational biomechanics community to analyze mathematical models described by sets of partial differential equations. FEM, however, has a number of fairly serious theoretical and practical deficiencies when applied to highly deformable objects of very complicated… More >

  • Open Access


    A Novel Boundary-Type Meshless Method for Solving the Modified Helmholtz Equation

    Jingen Xiao1,*, Chengyu Ku1,2

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 177-177, 2019, DOI:10.32604/icces.2019.05068

    Abstract This paper presents a novel boundary-type meshless method for solving the two-dimensional modified Helmholtz equation in multiply connected regions. Numerical approximation is obtained by the superposition principle of the non-singular basis functions satisfied the governing equation. The advantage of the proposed method is that the locations of the source points are not sensitive to the results. The novel concept may resolve the major issue for the method of fundamental solutions (MFS). In contrast to the collocation Trefftz method (CTM), the Trefftz order of the non-singular basis functions can be reduced since the multiple source points More >

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