A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids

Gu, Yuantong; Wang, Qianxi; Lam, Kwok‐Yan; Dai, K. Y.

doi:10.1016/j.enganabound.2006.12.008

Cited by 12 publications

(5 citation statements)

References 31 publications

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“…This value is called the critical failure load, and it is F=55.5 MN for this problem. Comparing with the FEM and other method results 10,12 , it can be seen that the results obtained by the present method are in good agreement with those obtained by other methods. It should be mentioned that the present method needs much less iteration steps than FEM.…”

Section: Numerical Examplesupporting

confidence: 77%

“…In the family of meshless methods, the meshless method based on the local weak-form is a welldeveloped technique including the meshless local Petrov-Galerkin (MLPG) method 8,9 and the local radial point interpolation method (LRPIM) 10 . Due to the stability and accuracy of MLS, the local meshless method based on the moving least squares (MLS) is becoming a robust numerical tool for the practical analysis.…”

Section: Y T Gumentioning

confidence: 99%

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An Elasto-Plastic Analysis of Solids by the Local Meshless Method Based on MLS

2008

Int. J. Mod. Phys. B

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A pseudo-elastic local meshless formulation is developed in this paper for elasto-plastic analysis of solids. The moving least square (MLS) is used to construct the meshless shape functions, and the weighted local weak-form is employed to derive the system of equations. Hencky's total deformation theory is applied to define the effective Young's modulus and Poisson's ratio in the nonlinear analysis, which are obtained in an iterative manner using the strain controlled projection method. Numerical studies are presented for the elasto-plastic analysis of solids by the newly developed meshless formulation. It has demonstrated that the present pseudo-elastic local meshless approach is very effective for the elastoplastic analysis of solids.

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Section: Numerical Examplesupporting

confidence: 77%

Section: Y T Gumentioning

confidence: 99%

An Elasto-Plastic Analysis of Solids by the Local Meshless Method Based on MLS

2008

Int. J. Mod. Phys. B

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“…A key feature of meshfree methods is that a predefined mesh is not necessary for field variable approximation/interpolation. Various meshfree algorithms have shown very good performance in handling mesh distortion for nonlinear problems [11][12][13][14][15][16][17][18][19]. However, there are still some open topics for nonlinear explicit dynamic analysis using meshfree methods, such as handling essential boundary conditions effectively, conducting numerical integration, and stable time step calculation.…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional nonlinear meshfree algorithm for simulating mechanical responses of soft tissue

Zhang

Wittek

Joldes

et al. 2014

Engineering Analysis with Boundary Elements

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This paper presents an effective three-dimensional (3D) nonlinear explicit dynamic meshfree algorithm for the simulation of soft tissue mechanical responses. In the algorithm soft tissues are considered to be hyperelastic and nearly incompressible materials. The algorithm is based on the element-free Galerkin (EFG) method using total Lagrangian formulation and moving least square (MLS) approximation. This approximation uses a relatively large number of nodes for shape functions creation, which can significantly delay mesh distortion in large deformation computations. Essential boundary conditions are imposed exactly by coupling MLS shape functions with a finite element (FE) interpolation in the close region of essential boundary. Although volumetric integration is not exact, the large support domains of the MLS shape functions alleviate some of the key weaknesses of FE methods such as hour-glassing and volumetric locking. Explicit integration is performed in time domain, using a recently proposed method to calculate the critical time step. Verification against the results obtained using the established nonlinear finite element procedures available in the ABAQUS code confirms the accuracy of the presented meshfree algorithm. Application of the algorithm in modeling of the brain indentation indicates its ability to facilitate robust and accurate prediction of the organ responses subjected to large localized deformations consistent with the loading due to surgery.

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“…한편, 약정식화(weak formulation)를 기반으로 무요소 근사함수를 이용하여 재료비선형 문제를 다룬 연구들은 다수 있다 (Gu et al, 2007;Pozo et al, 2009;Dai et al, 2006). 미분항은 나타나지 않는다.…”

Section: Mls 차분법의 근사함수는 요소를 사용하지 않기 때문에unclassified

Development of MLS Difference Method forMaterial Nonlinear Problem

Yoon¹

2016

jcoseik

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This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

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A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids

Cited by 12 publications

References 31 publications

An Elasto-Plastic Analysis of Solids by the Local Meshless Method Based on MLS

An Elasto-Plastic Analysis of Solids by the Local Meshless Method Based on MLS

A three-dimensional nonlinear meshfree algorithm for simulating mechanical responses of soft tissue

Development of MLS Difference Method forMaterial Nonlinear Problem

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