Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations

Atluri, Satya N.; Cho, Jin Yeon; Kim, H.-G.

doi:10.1007/s004660050456

Cited by 169 publications

(108 citation statements)

References 17 publications

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“…In the present paper, the local subdomains are taken to be of a quadrature shape. The local weak form [20] [21] of the governing Equation (25) can be written as: …”

Section: The Mlpg Weak Formulation In Laplace-transformed Domainmentioning

confidence: 99%

“…This method based on a local weak form and Moving Least Squares (MLS) approximation [15] [16] [17] [18]. The main advantage of this method over the widely used finite element methods (FEM) is that it does not need any mesh, either for the interpolation of the solution variables or for the integration of the weak forms [19] [20]. The MLPG method and its variations have been applied for elastodynamic and elastostatic problems by several authors.…”

Section: Introductionmentioning

confidence: 99%

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A Study of the Elastodynamic Problem by Meshless Local Petrov-Galerkin Method Using the Laplace-Transform

Eddaoudy¹,

Bouziane²

2018

WJM

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The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering; however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of

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“…In the present paper, the local subdomains are taken to be of a quadrature shape. The local weak form [20] [21] of the governing Equation (25) can be written as: …”

Section: The Mlpg Weak Formulation In Laplace-transformed Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Study of the Elastodynamic Problem by Meshless Local Petrov-Galerkin Method Using the Laplace-Transform

Eddaoudy¹,

Bouziane²

2018

WJM

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“…Frame bending is modeled as a 2D continuum problem under plane stress conditions. This was considered more suitable than formulating a 1D beam (as employed by Atluri et al (1999), Donning and Liu (1997), and Suetake (2002)) because MLS shape functions would need to have cubic consistency in order to approximate both the displacement and rotation deformation fields. This causes increased difficulties in the meshfree formulation when trying to enforce displacement and slope boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Meshfree Method for Inelastic Frame Analysis

2009

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The feasibility of using meshfree methods in nonlinear structural analysis is explored in an attempt to establish a new paradigm in structural engineering computation. A blended finite element and meshfree Galerkin approximation scheme is adopted to solve the inelastic response of plane frames. In the proposed method, moving least squares shape functions represent the displacement field, a plane stress approximation of the two-dimensional domain simulates beam bending, J2 plasticity characterizes material behavior and stabilized nodal integration yields the discrete equations. The particular case of steel frames composed of wide flange sections is investigated, though the concepts introduced can be extended to other structural materials and systems.Results of numerical simulations are compared with analytical solutions, finite element simulations and experimental data to validate the methodology. The findings indicate that meshfree methods offer an alternative approach with enhanced capabilities for nonlinear structural analysis. The proposed method can be integrated with finite elements so that a structural system is composed of mesh-free regions and finite-element regions to facilitate simulations of large-scale systems.

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“…Moreover, the EBCs were enforced by an auxiliary method which was not stated explicitly. Atluri et al [1999] extended the conventional moving least squares (MLS) interpolant, first presented by Lancaster and Salkauskas [1981], to Hermite-type interpolation and called it generalized MLS (GMLS). For illustration, Atluri et al [1999] considered a one-dimensional thin beam and imposed the EBC using the penalty method.…”

Section: Introductionmentioning

confidence: 99%

Gradient reproducing kernel particle method

Hashemian

Shodja

2008

JOMMS

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This paper presents an innovative formulation of the RKPM (reproducing kernel particle method) pioneered by Liu. A major weakness of the conventional RKPM is in dealing with the derivative boundary conditions. The EFGM (element free Galerkin method) pioneered by Belytschko shares the same difficulty. The proposed RKPM referred to as GRKPM (gradient RKPM), incorporates the first gradients of the function in the reproducing equation. Therefore in three-dimensional space GRKPM consists of four independent types of shape functions. It is due to this feature that the corrected collocation method can be readily generalized and combined with GRKPM to enforce the EBCs (essential boundary conditions), involving both the field quantity and its first derivatives simultaneously. By considering several plate problems it is observed that GRKPM yields solutions of higher accuracy than those obtained using the conventional approach, while for a desired accuracy the number of particles needed in GRKPM is much less than in the traditional methodology.

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Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations

Cited by 169 publications

References 17 publications

A Study of the Elastodynamic Problem by Meshless Local Petrov-Galerkin Method Using the Laplace-Transform

A Study of the Elastodynamic Problem by Meshless Local Petrov-Galerkin Method Using the Laplace-Transform

Meshfree Method for Inelastic Frame Analysis

Gradient reproducing kernel particle method

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