Direct meshless local Petrov–Galerkin method for elastodynamic analysis

Mirzaei, Davoud; Hasanpour, Kourosh

doi:10.1007/s00707-015-1494-0

Cited by 22 publications

(7 citation statements)

References 28 publications

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“…In [45], DMLPG method is applied for solving a two-dimensional time fractional advection-diffusion equation. An application to elastodynamic analysis can be found in [37]. Moreover, for the first time, in [39] Mirzaei and Schaback applied DMLPG for solving time-dependent problems.…”

Section: A Brief Review Of the Dmlpg Methodsmentioning

confidence: 98%

Application of direct meshless local Petrov–Galerkin (DMLPG) method for some Turing-type models

Ilati

Dehghan

2016

Engineering with Computers

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Section: A Brief Review Of the Dmlpg Methodsmentioning

confidence: 98%

Application of direct meshless local Petrov–Galerkin (DMLPG) method for some Turing-type models

Ilati

Dehghan

2016

Engineering with Computers

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“…Eventually the nodal displacement function can be expressed by substituting equations (11) and (13) into equation 2:…”

Section: Composite Shape Functions Based Onmentioning

confidence: 99%

“…Meshfree methods only employ nodes to discretize the problem domain and therefore are immune to mesh distortion problems. ey are suitable for solving complex practical problems such as large deformation, fracture propagation simulation, and impact-induced failure [6][7][8][9][10][11][12][13][14][15]. However, there exist important drawbacks for meshfree methods, such as the essential boundary condition implementation handicap, high computational cost, and complex trial function construction process, thereby giving rise to several hybrid schemes to enhance the applicability of meshfree methods.…”

Section: Introductionmentioning

confidence: 99%

FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis

Zhang

Chen

Qian

et al. 2019

Shock and Vibration

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The partition-of-unity method based on FE-Meshfree QUAD4 element synthesizes the respective advantages of meshfree and finite element methods by exploiting composite shape functions to obtain high-order global approximations. This method yields high accuracy and convergence rate without necessitating extra nodes or DOFs. In this study, the FE-Meshfree method is extended to the free and forced vibration analysis of two-dimensional solids. A modified radial point interpolation function without any supporting tuning parameters is applied to construct the composite shape functions. The governing equations of elastodynamic problem are transformed into a standard weak formulation and then discretized into time-dependent equations which are solved via Bathe time integration scheme to conduct the forced vibration analysis. Several numerical test problems are solved and compared against previously published numerical solutions. Results show that the proposed FE-Meshfree QUAD4 element owns greater tolerance for mesh distortion and provides more accurate solutions.

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“…Recently, some significant developments in meshless methods for solving linear and nonlinear partial differential equations have been achieved. For instance, the meshless local Petrov-Galerkin and local boundary integral equations methods were studied in [4,21,31]. These two methods basically transformed the original problem into a local weak formulation, and the shape functions were constructed from using the moving least-squares approximation to interpolate the solution variables.…”

Section: Introductionmentioning

confidence: 99%

A Runge–Kutta–Chebyshev SPH algorithm for elastodynamics

Seaı̈d

2016

Acta Mech

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A stable and accurate Smoothed Particle Hydrodynamics (SPH) method is proposed for solving elastodynamics in solid mechanics. The SPH method is mesh-free, and it promises to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes the SPH method very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, the conventional SPH method still has significant limitations that prevent its acceptance among researchers and engineers, namely the stability and computational costs. In approximating unsteady problems using the SPH method, attention should be given to the choice of time integration schemes as accuracy and efficiency of the SPH solution may be limited by the timesteps used in the simulation. This study presents an attempt to reconstruct an unconditionally stable SPH method for elastodynamics. To achieve this objective we implement an explicit Runge-Kutta Chebyshev scheme with extended stages in the SPH method. This time stepping scheme adds in a natural way a stabilizing stage to the conventional Runge-Kutta method using the Chebyshev polynomials. Numerical results are shown for several test problems in elastodynamics. For the considered elastic regimes, the obtained results demonstrate the ability of our new algorithm to better maintain the shape of the solution in the presence of shocks.

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Direct meshless local Petrov–Galerkin method for elastodynamic analysis

Cited by 22 publications

References 28 publications

Application of direct meshless local Petrov–Galerkin (DMLPG) method for some Turing-type models

Application of direct meshless local Petrov–Galerkin (DMLPG) method for some Turing-type models

FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis

A Runge–Kutta–Chebyshev SPH algorithm for elastodynamics

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