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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

A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples.

https://www.mdpi.com/2075-1680/9/3/92/pdf

A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

Abstract In this study, we present a displacement based polygonal finite element method for compressible and nearly-incompressible elastic solids undergoing large deformations in two dimensions. This is achieved by projecting the dilatation strain onto the linear approximation space, within the framework of volume averaged nodal projection method. To reduce the numerical integration burden over polytopes, a linear strain smoothing technique is employed to compute the terms in the bilinear/linear form. The salient features of the proposed framework are: (a) does not require derivatives of shape functions and complex numerical integration scheme to compute the bilinear and linear form and (b) volumetric locking is alleviated by adopting the volume averaged nodal projection technique. The efficacy, convergence properties and accuracy of the proposed framework is demonstrated through four standard benchmark problems.

A cell-based smoothed finite element method for finite elasticity

Mathematical Modelling and Artificial Intelligence in Luxembourg: Twenty PhD Students to be Trained in Data-Driven Modelling.

An analytical solution for the static bending of smart laminated composite and functionally graded plates with and without porosity

In this paper, an adaptive phase-field scaled boundary finite element method for fracture in functionally graded material (FGM) is presented. The model accounts for spatial variation in the materia...

Sundararajan Natarajan

Papers

A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

A cell-based smoothed finite element method for finite elasticity

Mathematical Modelling and Artificial Intelligence in Luxembourg: Twenty PhD Students to be Trained in Data-Driven Modelling.

An analytical solution for the static bending of smart laminated composite and functionally graded plates with and without porosity

Application of Adaptive Phase-Field Scaled Boundary Finite Element Method for Functionally Graded Materials