Meshfree method for large deformation analysis–a reproducing kernel particle approach

Liew, K.M.; Ng, TP; Wu, Yi-Chien

doi:10.1016/s0141-0296(01)00120-1

Cited by 103 publications

(37 citation statements)

References 35 publications

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“…This implies the first three properties of (16). If v ∈ U is admissible for the infimum in the third property, we can write v = v −ũ +ũ and…”

Section: Theoremmentioning

confidence: 89%

“…A good review on the method of fundamental solutions (MFS) can be found from [11]. The advantages of meshless computational methods, in particular the weak form, have further been verified by the works on solving large deformation problems due to nonlinear structure [8,30] and deformation behavior of smart material such as shape memory alloys [16]. Please refer to the survey paper [5] on the comparison between meshless method and traditional finite element and boundary element methods.…”

Section: Symmetric Meshless Kernel Methodsmentioning

confidence: 99%

“…The uniqueness ofũ with respect to the properties in (16) follows from the fact that the difference of two such functions must be in both U R(Λ) and U ⊥ Λ . 2…”

Section: Theoremmentioning

confidence: 99%

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Solvability of partial differential equations by meshless kernel methods

Hon

Schaback²

2006

Adv Comput Math

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“…This implies the first three properties of (16). If v ∈ U is admissible for the infimum in the third property, we can write v = v −ũ +ũ and…”

Section: Theoremmentioning

confidence: 89%

Section: Symmetric Meshless Kernel Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Solvability of partial differential equations by meshless kernel methods

Hon

Schaback²

2006

Adv Comput Math

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“…Meshfree methods might have merits in reducing the efforts for meshing and remeshing. To solve large deformation, meshfree methods have been employing the Lagrangian shape functions (sometimes denoted as material shape functions) [1][2][3][4][5]. The Lagrangian shape functions and their spatial derivatives are obtained by the transformation from the initial (deformation-free) meshfree shape functions using the current displacement field.…”

Section: Reshaping Of Nodal Supportsmentioning

confidence: 99%

“…Without remodelling, therefore, the analysis would fail when large deformation causes severe local distortion of the supports of meshfree shape functions. Since the first work by Chen et al appeared, several attempts have been made to solve plastic deformation with meshfree methods [2][3][4][5]. However, they all used the Galerkin formulation with the Lagrangian-type meshfree approximations.…”

Section: Introductionmentioning

confidence: 99%

The least‐squares meshfree method for elasto‐plasticity and its application to metal forming analysis

Kwon

Park

Youn

2005

Numerical Meth Engineering

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SUMMARYA new meshfree method for the analysis of elasto-plastic deformation is presented. The method is based on the proposed first-order least-squares formulation for elasto-plasticity and the moving leastsquares approximation. The least-squares formulation for classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformation are proposed. In the formulation, equilibrium equation and flow rule are enforced in least-squares sense, i.e. their squared residuals are minimized, and hardening law and loading/unloading condition are enforced pointwise at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. The proposed formulation is a mixed-type method since the residuals are represented in a form of first-order differential system using displacement and stress components as nodal unknowns. Also the penalty schemes for the enforcement of boundary and frictional contact conditions are devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near contact interface. The proposed method does not employ structure of extrinsic cells for any purpose. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed.

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Development of the distinct lattice spring model for large deformation analyses

Zhao

2013

Num Anal Meth Geomechanics

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SUMMARYThis study develops the distinct lattice spring model (DLSM) for geometrically nonlinear large deformation problems. The formulation of a spring bond deformation under a large deformation is derived under the Lagrange framework using polar decomposition. The results reveal that the DLSM's stiffness matrix under small deformations is the tangent stiffness matrix of the DLSM under large deformations. The formulation of the spring bond internal force under a given configuration is also presented and can be used to calculate the unbalanced force. Using these formulations, three nonlinear solving methods (the Euler method, modified Euler method, and Newton method) are developed for the DLSM with which to tackle large deformation problems. To investigate the performance of the developed model, three numerical examples involving large deformations are presented, the results of which are also in good agreement with the analytical and finite element method solutions. Copyright © 2013 John Wiley & Sons, Ltd.

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Meshfree method for large deformation analysis–a reproducing kernel particle approach

Cited by 103 publications

References 35 publications

Solvability of partial differential equations by meshless kernel methods

Solvability of partial differential equations by meshless kernel methods

The least‐squares meshfree method for elasto‐plasticity and its application to metal forming analysis

Development of the distinct lattice spring model for large deformation analyses

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