On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

Bordas, Stéphane; Kerfriden, Pierre; Augarde, Charles E.; Mahapatra, D. Roy; Rabczuk, Timon; Pont, Stefano Dal

doi:10.1002/nme.3156

Cited by 155 publications

(109 citation statements)

References 48 publications

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“…From the numerical study presented, it was concluded that the CS-FEM technique is robust, computationally inexpensive, free of locking and importantly insensitive to mesh distortions. In [2], CS-FEM has been combined with the extended FEM to study moving boundary problems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements

Natarajan

Ferreira

Bordas

et al. 2013

Composite Structures

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Section: Introductionmentioning

confidence: 99%

Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements

Natarajan

Ferreira

Bordas

et al. 2013

Composite Structures

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“…SFEMs using quadratic 8-node quadrilateral elements (Q8) does not pass the patch test [32]. Further investigation by authors showed the same shortcoming for quadratic 6-node triangular elements.…”

Section: Different Coupled Hydro-mechanical Sfem Modelsmentioning

confidence: 99%

Application of smoothed finite element method in coupled hydro-mechanical analyses

Karimian

Oliaei

2017

Scientia Iranica

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Smoothed finite element method (SFEM) was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. In this method, integration is performed on "smoothing domains" rather than elements. Smoothing domains are created based on cells, nodes or edges for two dimensional problems. Based on the smoothing domain creation method, different types of SFEM are developed that have different properties. It has been shown that these methods are insensitive to mesh distortion and are generally more computationally efficient than mesh-free and finite element methods for the same accuracy level. Because of their interesting features, they have been used to solve different problems. This paper investigates the performance of these methods in coupled hydro-mechanical (consolidation) analysis, by solution of some problems using a developed SFEM/FEM code. Biot's consolidation theory is reviewed, and after introduction of the idea and formulation of SFEMs, discretized form of equations is given. Requirements for creation of stable coupled hydro-mechanical models are discussed and based on them, two methods for creation of stable SFEM models are introduced. To investigate the effectiveness of the methods, a number of examples are solved and results are compared with the finite element and analytical ones.

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“…where is the standard deviation of the th variable, is the arbitrary factor, and the initial value range is (1,3). The computational formula is as follows:…”

Section: Sampling Of Classical Rsmmentioning

confidence: 99%

A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application

Meng

Jing

Zhang

et al. 2014

Advances in Mechanical Engineering

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A response surface method based on the all sample point interpolation approach (ASPIA) is proposed to improve the efficiency of reliability computation. ASPIA obtains new sample points through linear interpolation. These new sample points are occasionally extremely dense, thus easily generating an ill-conditioned problem for approximation functions. A mobile most probable failure point strategy is used to solve this problem. The advantage of the proposed method is proven by two numerical examples. With the ASPIA, the approximated process can rapidly approach the actual limit equation with accuracy. Additionally, there are no difficulties in applying the proposed ASPIA to the response surface model with or without cross terms. Solution results for the numerical examples indicate that the use of the response surface function with cross terms increases time cost, but result accuracy cannot be improved significantly. Finally, the proposed method is successfully used to analyze the reliability of the hydraulic cylinder of a forging hydraulic press by combining MATLAB and ANSYS software. The engineering example confirms the practicality of this method.

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On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

Cited by 155 publications

References 48 publications

Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements

Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements

Application of smoothed finite element method in coupled hydro-mechanical analyses

A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application

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