A meshless local natural neighbor interpolation method for two-dimension incompressible large deformation analysis

Zhu, Hehua; Liu, Wenjun; Cai, Yongchang; Yuanbin, Miao

doi:10.1016/j.enganabound.2007.02.003

Cited by 14 publications

(4 citation statements)

References 13 publications

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“…where S is the flexibility matrix, S = D −1 , and D is shown in (10) and (11); (⋅) 0 give the values of every variation in the initial state;Ḟ is the body force column vector; andṪ is the surface force column vector.…”

Section: Incremental Hybrid Natural Elementmentioning

confidence: 99%

“…Ding et al [10] formatted elastoplasticity natural element method and calculated actual engineering problems. Hehua et al [11] utilized the meshless local natural neighbor interpolation method (MLNNIM) to solve problems of two-dimensional elastoplastic large deformation. In recent years, with the development of the numerical methods, other meshless methods [12][13][14] have been used to solve the elastoplasticity problems.…”

Section: Introductionmentioning

confidence: 99%

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The Incremental Hybrid Natural Element Method for Elastoplasticity Problems

Dong

Zhou

et al. 2014

Mathematical Problems in Engineering

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An incremental hybrid natural element method (HNEM) is proposed to solve the two-dimensional elasto-plastic problems in the paper. The corresponding formulae of this method are obtained by consolidating the hybrid stress element and the incremental Hellinger-Reissner variational principle into the NEM. Using this method, the stress and displacement variables at each node can be directly obtained after the stress and displacement interpolation functions are properly constructed. The numerical examples are given to show the advantages of the proposed algorithm of the HNEM, and the solutions for the elasto-plastic problems are better than those of the NEM. In addition, the performance of the proposed algorithm is better than the recover stress method using moving least square interpolation.

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Section: Incremental Hybrid Natural Elementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Incremental Hybrid Natural Element Method for Elastoplasticity Problems

Dong

Zhou

et al. 2014

Mathematical Problems in Engineering

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“…NURBS-based finite element isogeometric analysis introduced by Hughes et al [25] is able to describe exactly geometry with curved boundary. Meshfree approach [26][27][28] in which the mesh connect data point condition is released is also powerful in simulating the geometry of complex objects containing cracks.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations

Le-Manh

Luu-Anh

Lee

2015

Mechanics of Advanced Materials and Structures

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A large deformation theory, so-called Green strains with small rotations, is proposed and employed for flexural analysis of composite plates. Isogeometric analysis cooperated with firstorder shear deformation theory is used to derive finite element models. Strain-displacement relations in sense of von-Karman theory and the proposed theory are formulated. Shear locking phenomenon is avoided by using reduced integration technique. Newton-Raphson method is employed for nonlinear analysis procedure. Numerical examples including isotropic and laminated composite plates under different boundary conditions are investigated. The results have been verified with those available in literature and show the advantages of the proposed strain theory.

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“…27. External cables have been added to the representation, although their flexibility is not considered in order to 7.2.…”

Section: B 3d Modelsmentioning

confidence: 99%

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Ibáñez¹

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A meshless local natural neighbor interpolation method for two-dimension incompressible large deformation analysis

Cited by 14 publications

References 13 publications

The Incremental Hybrid Natural Element Method for Elastoplasticity Problems

The Incremental Hybrid Natural Element Method for Elastoplasticity Problems

Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations

On the application of meshfree methods to the nonlinear dynamics of multibody systems

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