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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

Layup optimization of tow-steered composite laminates for maximum fundamental frequency and flutter speed using differential evolution

Bayesian inference is a powerful technique for damage/flaw detection in critical structures. This paper explores the application of Bayesian inference to identify the flaws (voids/inclusions) and its parameters, assuming no information about the flaws is known a priori. Multiple flaws are represented by a parameter vector that contains the locations and the geometric information. In the inverse problem framework, the Scaled Boundary Finite Element Method (SBFEM) with quadtree decomposition is used to solve the forward problem. The flaw parameters are statistically quantified using the Bayesian inference. The likelihood function and prior information update the joint distribution of the number of flaws and their corresponding flaw parameters. The sampling to estimate the posterior distribution of the flaw parameters is based on the trans-dimensional Reversible Jump Markov Chain Monte Carlo (RJMCMC). Also, the impact of additive Gaussian noise on the observed data is investigated. Numerical examples include identifying multiple voids of different shapes such as circle and ellipse and identifying voids and inclusions, using the proposed approach with input sensor data at different noise levels. 

SBFEM and Bayesian inference for efficient multiple flaw detection in structures

A cell-based smoothed finite-element method for gradient elasticity

In this paper, a h-adaptive methodology based on the polytopal meshes is proposed for capturing high stress gradients at the materials corners and the stress singularities at the vicinity of a crack tip. The adaptive refinement is based on the error indicator directly computed from the displacement solutions of the scaled boundary finite element method. Based on the error indicator, a polygon of n-sides which has an error exceeding a specified tolerance is subdivided recursively into $$(n+1)$$
 child polygons. The salient features of the proposed framework are: (a) circumvents a need for post-processing techniques for error estimation; (b) elements with hanging nodes are treated as polygons without a need for special treatment and (c) stress gradients and stress singularities are accurately captured due to the semi-analytical formulation. The robustness and the convergence properties of the proposed framework is demonstrated with three benchmark examples.

Sundararajan Natarajan

Papers

Layup optimization of tow-steered composite laminates for maximum fundamental frequency and flutter speed using differential evolution

SBFEM and Bayesian inference for efficient multiple flaw detection in structures

A cell-based smoothed finite-element method for gradient elasticity

An adaptive polytree approach to the scaled boundary boundary finite element method

Simulating Isochromatic Fringes from Finite Element Results of FEniCS