Galerkin based smoothed particle hydrodynamics

Wong, Simon H.F.; Shie, Y.

doi:10.1016/j.compstruc.2009.04.010

Cited by 9 publications

(3 citation statements)

References 57 publications

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“…This acceleration correction term was further optimised for hypervelocity impact problems in [37,38], where high frequency spurious oscillations are often observed, particularly for shocks and sharp discontinuities. A novel Galerkin SPH formulation was proposed in [41,42] for large deformation structural mechanics applications. This method employs a moving-least-squares approximation along with stabilised nodal integration.…”

Section: Different Variants Of the Sph Methodsmentioning

confidence: 99%

Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

Das

Cleary

2014

J Sci Comput

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The accuracy and stability of the classical formulation of the smoothed particle hydrodynamics (SPH) method for modelling compression of elastic solids is studied to assess its suitability for predicting solid deformation. SPH has natural advantages for simulating problems involving compression of deformable solids arising from its ability to handle large deformation without re-meshing, complex free surface behaviour and tracking of multiple material interfaces. The 'classical SPH method', as originally proposed by Monaghan (in Ann Rev Astron 30: 543-574, 1992, Rep Prog Phys 68:1703-1759, 2005, has become broadly established as a robust method in different areas, especially involving fluid flows. However, limited attention has been paid to understanding of its numerical performance for elastic deformation problems. To address this, we evaluate the classical SPH method to explore its stability, accuracy and convergence and the effect of numerical parameters on elastic solutions using a generic uniaxial stress test. Short term transient and long term uniform state SPH solutions agree well with those from the finite element method (FEM). The SPH elastic deformation solution showed good convergence with increasing particle resolution. The tensile instability stabilisation method was found to have little impact on the solution, except for higher values of the correction factor which then produce small amplitude benign artificial banded stress patterns. The use of artificial viscosity is able to eliminate the instability and improve the accuracy of the solutions. Overall, the classical SPH method appears to be robust and suitable for accurate modelling of elastic solids under compression.

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Section: Different Variants Of the Sph Methodsmentioning

confidence: 99%

Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

Das

Cleary

2014

J Sci Comput

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“…In recent years, a number of researchers have investigated accuracy improvement of SPH. Wong and Shie developed a Galerkin‐based SPH formulation with moving least‐squares approximation in combination with updated Lagrangian kernel functions to remove instabilities. They applied it to impact problems with large deformation.…”

Section: Introductionmentioning

confidence: 99%

Smoothed particle hydrodynamics in a generalized coordinate system with a finite‐deformation constitutive model

Yashiro

Okabe

2015

Numerical Meth Engineering

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SUMMARYThis study proposes smoothed particle hydrodynamics (SPH) in a generalized coordinate system. The present approach allocates particles inhomogeneously in the Cartesian coordinate system and arranges them via mapping in a generalized coordinate system in which the particles are aligned at a uniform spacing. This characteristic enables us to employ fine division only in the direction required, for example, in the through‐thickness direction for a thin‐plate problem and thus to reduce computation cost. This study provides the formulation of SPH in a generalized coordinate system with a finite‐deformation constitutive model and then verifies it by analyzing quasi‐static and dynamic problems of solids. High‐velocity impact test was also performed with an aluminum target and a steel sphere, and the predicted crater shape agreed well with the experiment. Furthermore, the numerical study demonstrated that the present approach successfully reduced the computation cost with marginal degradation of accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Major contributions have included the work of Hibbitt et al , Bathe et al and Bathe and Ozdemir , adopting the Total Lagrangian (TL) approach; McMeeking and Rice and Kojic and Bathe , proposing the Updated Lagrangian (UL) framework; and Hughes and Winget , Haber and Gadala and Wang , who introduced the ALE technique. Other methods of large deformation analysis include finite difference method , smooth particle hydrodynamics , reproducing kernel particle method and particle simulation method , among others.…”

Section: Introductionmentioning

confidence: 99%

An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method

Khoshghalb

Khalili

2015

Num Anal Meth Geomechanics

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Summary An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

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Galerkin based smoothed particle hydrodynamics

Cited by 9 publications

References 57 publications

Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

Evaluation of Accuracy and Stability of the Classical SPH Method Under Uniaxial Compression

Smoothed particle hydrodynamics in a generalized coordinate system with a finite‐deformation constitutive model

An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method

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