Meshfree and particle methods and their applications

Li, Shaofan; Liu, Wing Kam

doi:10.1115/1.1431547

Cited by 748 publications

(444 citation statements)

References 139 publications

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“…In meshless methods (MMs) there is no need to construct a mesh, as in finite element method (FEM), which is often in conflict with the real physical compatibility condition that a continuum possesses [1]. Moreover, stresses obtained using FEM are discontinuous and less accurate while a considerable loss of accuracy is observed when dealing with large deformation problems because of element distortion.…”

Section: Introductionmentioning

confidence: 99%

Stiffness Matrix Computation for Element Free Galerkin Methods on Gpu

Karatarakis¹,

Metsis²,

Papadrakakis³

2013

Proceedings of the 3rd South-East European Conference on Computational Mechanics – SEECCM III

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Section: Introductionmentioning

confidence: 99%

Stiffness Matrix Computation for Element Free Galerkin Methods on Gpu

Karatarakis¹,

Metsis²,

Papadrakakis³

2013

Proceedings of the 3rd South-East European Conference on Computational Mechanics – SEECCM III

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“…Recall that most meshfree methods need to resort to special techniques to enforce essential boundary conditions (for example, see Refs. [55,56,57]). Recently, new applications of max-ent meshfree basis functions have emerged: co-rotational formulation is presented in Ref.…”

Section: Maximum-entropy Basis Functionsmentioning

confidence: 99%

Maximum-entropy meshfree method for compressible and near-incompressible elasticity

Ortiz

Puso

Sukumar

2010

Computer Methods in Applied Mechanics and Engineering

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Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a lockingfree small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximumentropy meshfree formulation.

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“…Another method to maintain the usual convergence rate by hierarchical enrichment was proposed by Wagner and Liu [48] and Han et al [18]. Other good overviews about meshfree and particle methods, their coupling to finite elements with impressive examples can be found in Li and Liu [31,32].…”

Section: Introductionmentioning

confidence: 99%

Coupling of mesh-free methods with finite elements: basic concepts and test results

Rabczuk

Xiao

Sauer

2006

Commun. Numer. Meth. Engng.

182

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SUMMARYThis paper reviews several novel and older methods for coupling meshfree particle methods, particularly the elementfree Galerkin (EFG) method and the Smooth Particle Hydrodynamics (SPH), with finite elements. We study master slave couplings where particles are fixed across the finite element boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent from the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods.

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Meshfree and particle methods and their applications

Cited by 748 publications

References 139 publications

Stiffness Matrix Computation for Element Free Galerkin Methods on Gpu

Stiffness Matrix Computation for Element Free Galerkin Methods on Gpu

Maximum-entropy meshfree method for compressible and near-incompressible elasticity

Coupling of mesh-free methods with finite elements: basic concepts and test results

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