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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

Abstract The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen’s nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

On the application of the partition of unity method for nonlocal response of low-dimensional structures

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D.

/pdf/on-the-equivalence-between-the-cell-based-smoothed-finite-ftdz9dlpn0.pdf

On the equivalence between the cell-based smoothed finite element method and the virtual element method

In this paper, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range in two and three ...

Scaled Boundary Finite Element Method for Mid-Frequency Acoustics of Cavities

In this paper, the cell-based smoothed finite element method is extended to solve stochastic partial differential equations with uncertain input parameters. The spatial field of Young’s Modulus and...

/pdf/a-stochastic-galerkin-cell-based-smoothed-finite-element-3md87uw553.pdf

Sundararajan Natarajan

Papers

On the application of the partition of unity method for nonlocal response of low-dimensional structures

On the equivalence between the cell-based smoothed finite element method and the virtual element method

Scaled Boundary Finite Element Method for Mid-Frequency Acoustics of Cavities

A stochastic Galerkin cell-based smoothed finite element method (SGCS-FEM)

An explicit methodology of random fibre modelling for FRC fracture using non-conforming meshes and cohesive interface elements