On the Development of a Hybrid Particle Method Using the Differential Formulation

Dyka, C. T.; Saigal, Sunil

doi:10.1080/15502280590888621

Cited by 5 publications

(10 citation statements)

References 19 publications

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“…These are the motion points (mps) and the stress points (sps), respectively. An example of the distribution of stress and motion points [12] for a 2-D solid is illustrated in Figure 1. The motion points are locations where the momentum is balanced and where the accelerations, velocities and displacements are computed directly using the central difference method.…”

Section: The Hpm Formulationmentioning

confidence: 99%

“…The motion points are locations where the momentum is balanced and where the accelerations, velocities and displacements are computed directly using the central difference method. The stress points are locations where velocities are obtained either explicitly through direct interpolation from the surrounding motion point neighbourhood, or parametrically if the stress points are located within pseudo cells formed by motion points [12]. Stress histories are tracked at both the stress and motion points, respectively.…”

Section: The Hpm Formulationmentioning

confidence: 99%

“…In Reference [20], Type A and Type B MLS interpolants are known as nodal approximation and pointwise approximation, respectively. A detailed discussion on the use of these two types of MLS interpolants in finding the required derivatives in HPM can be found in Reference [12].…”

Section: Type a And Type B Mls Interpolantsmentioning

confidence: 99%

“…Comprehensive reviews on these methods and their derivatives can be found in References [7][8][9][10][11]. The hybrid particle method (HPM) [12,13] is a recently developed particle method, and is based on the strong form of the conservation equations. This method employs two sets of particles, known as the motion points and the stress points, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…This method employs two sets of particles, known as the motion points and the stress points, respectively. The use of stress points in particle methods has been shown to increase both stability [14][15][16] and accuracy [12] over co-locational particle methods, such as the classical SPH. In the HPM, stresses are tracked at both the motion and the stress points.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Moving least-square interpolants in the hybrid particle method

Huang¹,

Saigal²,

Dyka³

2005

Int. J. Numer. Meth. Engng

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SUMMARYThe hybrid particle method (HPM) is a particle-based method for the solution of high-speed dynamic structural problems. In the current formulation of the HPM, a moving least-squares (MLS) interpolant is used to compute the derivatives of stress and velocity components. Compared with the use of the MLS interpolant at interior particles, the boundary particles require two additional treatments in order to compute the derivatives accurately. These are the rotation of the local co-ordinate system and the imposition of boundary constraints, respectively.In this paper, it is first shown that the derivatives found by the MLS interpolant based on a complete polynomial are indifferent to the orientation of the co-ordinate system. Secondly, it is shown that imposing boundary constraints is equivalent to employing ghost particles with proper values assigned at these particles. The latter can further be viewed as placing the boundary particle in the centre of a neighbourhood that is formed jointly by the original neighbouring particles and the ghost particles. The benefit of providing a symmetric or a full circle of neighbouring points is revealed by examining the error terms generated in approximating the derivatives of a Taylor polynomial by using a linear-polynomial-based MLS interpolant.Symmetric boundaries have mostly been treated by using ghost particles in various versions of the available particle methods that are based on the strong form of the conservation equations. In light of the equivalence of the respective treatments of imposing boundary constraints and adding ghost particles, an alternative treatment for symmetry boundaries is proposed that involves imposing only the symmetry boundary constraints for the HPM. Numerical results are presented to demonstrate the validity of the proposed approach for symmetric boundaries in an axisymmetric impact problem.

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Section: The Hpm Formulationmentioning

confidence: 99%

Section: The Hpm Formulationmentioning

confidence: 99%

Section: Type a And Type B Mls Interpolantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Moving least-square interpolants in the hybrid particle method

Huang¹,

Saigal²,

Dyka³

2005

Int. J. Numer. Meth. Engng

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Hybrid particle methods in frictionless impact‐contact problems

Huang¹,

Dyka²,

Saigal³

2004

Numerical Meth Engineering

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SUMMARYThe dual particle dynamic (DPD) methods which employ two sets of particles have been demonstrated to have better accuracy and stability than the co-locational particle methods, such as the smooth particle hydrodynamics (SPH). The hybrid particle method (HPM) is an extension of the DPD method. Besides the advantages of the DPD method, the HPM possesses features which better facilitate the simulation of large deformations. This paper presents the continued development of the HPM for the numerical solution of two-dimensional frictionless contact problems. The interface contact force algorithm which employs a modified kinematic constraints method is used to determine the contact tractions. In this method, both the impenetrability condition and the traction condition are simultaneously enforced. In the original kinematic constraints method, only the former condition is satisfied. A new formulation to find stress derivatives at stress-free corners by imposing stress-free boundary conditions is also developed. The results for 1-D and 2-D contact problems indicate good accuracy for the contact formulation as well as the corner treatment when compared to analytical solutions and explicit finite element results using the commercial code LS-DYNA.

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A Meshless Local Petrov-Galerkin (MLPG) Approach Based on the Regular Local Boundary Integral Equation for Linear Elasticity

Zhu

Zhang

Wang

2007

International Journal for Computational Methods in Engineering

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The moving local Petrov-Galerkin (MLPG) approach based on a regular local boundary integral equation (RLBIE) to solve problems in elasto-statics is developed. The present method is a truly meshless method, as absolutely no mesh connectivity is required for interpolating the solution variables and for integrating the weak form. Compared to the original MLPG method, the present method does not need the derivatives of the shape functions in constructing the stiffness matrix for those nodes with no displacement specified on their local boundaries. The numerical examples presented in the paper show that high rates of convergence with mesh refinement for the displacement and energy norms are achievable.

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On the Development of a Hybrid Particle Method Using the Differential Formulation

Cited by 5 publications

References 19 publications

Moving least-square interpolants in the hybrid particle method

Moving least-square interpolants in the hybrid particle method

Hybrid particle methods in frictionless impact‐contact problems

A Meshless Local Petrov-Galerkin (MLPG) Approach Based on the Regular Local Boundary Integral Equation for Linear Elasticity

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