Author
Sundararajan Natarajan
Other affiliations: GE Aviation, Bauhaus University, Weimar, University of New South Wales ...read more
Bio: Sundararajan Natarajan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Finite element method & Smoothed finite element method. The author has an hindex of 34, co-authored 181 publications receiving 4087 citations. Previous affiliations of Sundararajan Natarajan include GE Aviation & Bauhaus University, Weimar.
Papers
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TL;DR: In this paper, a mesh-free Galerkin method for the solution of Reissner-Mindlin plate problems is proposed, which is written in terms of the primitive variables only (i.e., rotations and transverse displacement).
6 citations
TL;DR: In this paper, a new Virtual Element Method (VEM) of arbitrary order k ≥ 2 for the time dependent Navier-Stokes equations in stream-function form is proposed and analyzed.
Abstract: In this work, a new Virtual Element Method (VEM) of arbitrary order k ≥ 2 for the time dependent Navier–Stokes equations in stream-function form is proposed and analyzed. Using suitable projection operators, the bilinear and trilinear terms are discretized by only using the proposed degrees of freedom associated with the virtual space. Under certain assumptions on the computational domain, error estimations are derived and shown that the method is optimally convergent in both space and time variables. Finally, to justify the theoretical analysis, four benchmark examples are examined numerically.
6 citations
TL;DR: The scaled boundary finite element method is extended to solve the second order elliptic equation with discontinuous coefficients and to treat weak discontinuities to show the robustness, accuracy and effectiveness of the proposed approach in modelling materials with interfaces.
6 citations
TL;DR: In this article, a non-intrusive scaled boundary finite element method to consider multiple input uncertainties, viz., material and geometry, is presented, which does not require explicit generation of a conforming mesh or special enrichment techniques.
5 citations
TL;DR: A semi-analytical solution is sought in the region close to the vicinity of the crack tip using the scaled boundary finite element method (SBFEM), whilst, the ESFEM is used for the rest of the domain this paper.
Abstract: This paper presents a technique to evaluate the fracture parameters by combining the edge based smoothed finite element method (ESFEM) and the scaled boundary finite element method (SBFEM). A semi-analytical solution is sought in the region close to the vicinity of the crack tip using the SBFEM, whilst, the ESFEM is used for the rest of the domain. As both methods satisfy the partition of unity and the compatibility condition, the stiffness matrices obtained from both methods can be assembled as in the conventional finite element method. The stress intensity factors (SIFs) are computed directly from their definition. Numerical examples of linear elastic bodies with cracks are solved without requiring additional post-processing techniques. The SIFs computed using the proposed technique are in a good agreement with the reference solutions. A crack propagation study is also carried out with minimal local remeshing to show the robustness of the proposed technique. The maximum circumferential stress criterion is used to predict the direction of propagation.
5 citations
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31 Oct 2001
TL;DR: The American Society for Testing and Materials (ASTM) as mentioned in this paper is an independent organization devoted to the development of standards for testing and materials, and is a member of IEEE 802.11.
Abstract: The American Society for Testing and Materials (ASTM) is an independent organization devoted to the development of standards.
3,792 citations
TL;DR: An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented in this article, which enables accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements.
Abstract: 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.
1,228 citations
TL;DR: This manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate the discourse.
1,088 citations
TL;DR: The essential ingredients in the Virtual Element Method for a simple linear elliptic second-order problem are presented and its computer implementation is emphasized to enable interested readers to readily implement the method.
Abstract: 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.
582 citations
TL;DR: A review of carbon nanotube reinforced composite (CNTRC) materials can be found in this article, where the concept of functionally graded (FG) pattern of reinforcement has been applied for functionally graded carbon nanite reinforced composite materials.
541 citations