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American Society for Testing and Materials

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems. Copyright © 2010 John Wiley & Sons, Ltd.

The extended/generalized finite element method: An overview of the method and its applications

https://orbilu.uni.lu/bitstream/10993/13726/1/phu-meshless.pdf

Review: Meshless methods: A review and computer implementation aspects

We present the essential ingredients in the Virtual Element Method for a simple linear elliptic second-order problem. We emphasize its computer implementation, which will enable interested readers to readily implement the method.

http://arturo.imati.cnr.it/brezzi/papers/hitchhikers-preprint.pdf

The Hitchhiker's Guide to the Virtual Element Method

Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review

In this paper, the flutter behaviour of simply supported square functionally graded material plates immersed in a supersonic flow is studied. An enriched 4-noded quadrilateral element based on field consistency approach is used for this study and the crack is modelled independent of the underlying mesh. The material properties are assumed to be temperature dependent and graded only in the thickness direction. The effective material properties are estimated using the rule of mixtures. The formulation is based on the first order shear deformation theory and the shear correction factors are evaluated employing the energy equivalence principle. The influence of the crack length, the crack orientation, the flow angle and the gradient index on the aerodynamic pressure and the frequency are numerically studied. The results obtained here reveal that the critical frequency and the critical pressure decreases with increase in crack length and it is minimum when the crack is aligned to the flow angle.

Supersonic flutter analysis of thin cracked functionally graded material plates

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method (SFEM) [3, 4, 5, 6, 7, 8, 9] and resolve the existence, linearity and positivity deficiencies pointed out in [1]. We show that Wachspress interpolants [10] computed in the physical coordinate system are very well suited to the SFEM, especially when elements are heavily distorted (obtuse interior angles). The proposed approximation leads to results which are almost identical to those of the SFEM initially proposed in [3]. These results that the proposed approximation scheme forms a strong and rigorous basis for construction of smoothed finite element methods.

On the approximation in the smoothed finite element method (SFEM)

Application of Discrete Shear Quadrilateral element for static bending, free vibration and buckling analysis of Functionally Graded Material plate

In this paper, the performance of different structural models based on global approach in evaluating the static response of curvilinear fibre composite laminates is analyzed. A Co shear flexible Quad-8 element developed based on higher-order structural theory is employed for the present study. The structural theory accounting for the realistic variation of displacements through the thickness and the possible discontinuity in the slope at the interface is considered. Four alternate discrete structural models, deduced from the generic structural model by retaining various terms in the displacement functions are examined for their applicability. The accuracy of the present formulation is demonstrated considering the problems for which analytical solutions are available. A systematic numerical study, assuming different ply-angle and lay-up, is conducted in bringing out the influence of various structural models on the static response of composite laminates with curvilinear fibres.

Sundararajan Natarajan

Papers

Supersonic flutter analysis of thin cracked functionally graded material plates

On the approximation in the smoothed finite element method (SFEM)

Application of Discrete Shear Quadrilateral element for static bending, free vibration and buckling analysis of Functionally Graded Material plate

Assessment of certain higher-order structural models based on global approach for bending analysis of curvilinear composite laminates

Effects of stress-diffusion interactions in an isotropic elastic medium in the presence of geometric discontinuities