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Sundararajan Natarajan

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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Posted ContentDOI
07 Dec 2019
TL;DR: In this article, a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems is presented.
Abstract: This work presents a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme for strain-smoothed finite element method (S-FEM) is no subdivision of finite element cells to sub-cells while the classical S-FEM needs sub-cells. Since the linear smoothing function is employed, S-FEM is able to use quadratic triangular or quadrilateral elements. The modified smoothed matrix obtained node-wise is evaluated. In the same manner with the computation of the strain-displacement matrix, the smoothed stiffness matrix and deformation graident are obtained over smoothing domains. A series of benchmark tests are investigated to demonstrate validity and stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using 2nd-order triangular element and the exact solutions.

2 citations

Journal ArticleDOI
TL;DR: In this article , a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate was considered and a conforming virtual element method (VEM) of arbitrary order was proposed to approximate the model problem numerically.
Abstract: In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose $$C^1$$ conforming virtual element method (VEM) of arbitrary order, $$k\ge 2$$ , to approximate the model problem numerically. We employ VEM to discretize the space variable and fully implicit scheme for temporal variable. Well-posedness of the fully discrete scheme is proved under certain conditions on the physical parameters, and we derive optimal order of convergence in both space and time variable. Finally, numerical experiments are presented to illustrate the behaviour of the proposed numerical scheme.

2 citations

01 Jan 2008
TL;DR: In this paper, the extended finite element method (XFEM) has been used for three dimensional crack propagation analysis of complex structures and has been shown to be a valid alternative to remeshing for crack propagation problems.
Abstract: The extended finite element method (XFEM) has emerged as a valid alternative to remeshing for crack propagation problems [1,2] and is now employed with success for three dimensional crack propagation analysis of complex structures [5,6].

2 citations

Journal ArticleDOI
TL;DR: In this paper, one of the variants of the smoothed finite element method, α-FEM is adopted for hyperelastic material with large deformation and contact nonlinearity in two dimensions.
Abstract: In this paper, one of the variants of the smoothed finite element method, α-FEM is adopted for hyperelastic material with large deformation and contact nonlinearity in two dimensions. The salient f...

2 citations

Journal ArticleDOI
01 Jan 2022
TL;DR: In this paper , a modified cell-based smoothed finite element method (S-FEM) was employed for topology optimization with the domain discretized with arbitrary polygons.
Abstract: The aim of this work is to employ a modified cell-based smoothed finite element method (S-FEM) for topology optimization with the domain discretized with arbitrary polygons. In the present work, the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM. This improves the accuracy and yields an optimal convergence rate. The gradients are smoothed over each smoothing domain, then used to compute the stiffness matrix. Within the proposed scheme, an optimum topology procedure is conducted over the smoothing domains. Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain. Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence, efficiency and accuracy.

1 citations


Cited by
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Reference EntryDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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