A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes

Nguyen-Thoi, T.; Vu-Do, H. C.; Rabczuk, Timon; Nguyen‐Xuan, H.

doi:10.1016/j.cma.2010.06.017

Cited by 152 publications

(56 citation statements)

References 33 publications

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“…Several theoretical aspects of the S-FEM models have been provided in [54,55]. The S-FEM models have also been further investigated and applied to various problems such as plates and shells [56][57][58][59][60][61][62][63][64][65][66][67][68], piezoelectricity [69,70], fracture mechanics [71], visco-elastoplasticity [72][73][74], limit and shakedown analysis for solids [75][76][77], and some other applications [78,79].…”

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confidence: 99%

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

Nguyen-Thoi

Phung‐Van

Canh

2014

Asia Pac. J. Comput. Engin.

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Background: The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion. Methods: The cell-based smoothed three-node Mindlin plate element (CS-MIN3) is combined with a second-order cone optimization programming (SOCP) to determine the upper bound limit load of the Mindlin plates. In the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the gradient matrices of MIN3 is used to compute the strain rates. Then the gradient smoothing technique on whole the triangular element is used to smooth the strain rates on these three sub-triangles. The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work. For Mindlin plates, the dissipation power is computed on both the middle plane and thickness of the plate. This minimization problem then can be transformed into a form suitable for the optimum solution using the SOCP. Results and Conclusions: The numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for both thick and thin plates.

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confidence: 99%

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

Nguyen-Thoi

Phung‐Van

Canh

2014

Asia Pac. J. Comput. Engin.

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“…N , N Φ , and N Ψ were expressed in similar shape functions. Four-node element divided into four smoothing subdomains [27], field nodes, edge smoothing nodes, center smoothing nodes, edge Gaussian point, outer normal vector distribution, and shape function values are shown in Figure 3.…”

Section: Ics-femmentioning

confidence: 99%

“…To overcome these limitations, a series of cell-based smoothed FEM (CS-FEM) [20][21][22][23][24][25][26] and node-based, edge-based, or facebased smoothed FEMs [27][28][29][30][31][32] were proposed. In recent years, many CS-FEM-based formulations were proposed.…”

Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

Cai

Meng

Wang

2018

Shock and Vibration

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To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

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“…The method was further extended to more complicated viscoelastoplastic analyses of 3D solids using the von-Mises yield function and the Prandtl-Reuss flow rule. A node-based smoothed finite element method was also proposed by Nguyen-Thoi et al [21] for the solid mechanics problems. The system stiffness matrix was computed using the smoothed strains over the smoothing domains associated with nodes of the element mesh.…”

Section: Introductionmentioning

confidence: 99%

An Effective Computational Approach for the Numerical Simulation of Elasto-/Viscoplastic Solid Materials

Angelis

2014

Advances in Mechanical Engineering

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The effects of different loading programs on the elasto-/viscoplastic behavior of rate-sensitive materials are analyzed with specific numerical examples. An appropriate solution scheme and a consistent tangent operator are applied which are capable of being adopted for general computational procedures. Numerical computations and results are reported which illustrate the ratedependence of the elasto-/viscoplastic constitutive model in use. In the numerical analysis the loading is applied by increasing the pressure and accordingly a nondimensional loading program parameter is introduced. In the numerical results the significance of the loading program is thus emphasized with reference to the nonlinear response of the elasto-/viscoplastic material behavior of solids.

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A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes

Cited by 152 publications

References 33 publications

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

An Effective Computational Approach for the Numerical Simulation of Elasto-/Viscoplastic Solid Materials

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