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: The relative performance between the approaches, the convergence properties and the accuracy is presented for two dimensional numerical examples, which shows that the proposed framework yields accurate results and converges at optimal convergence rate.
5 citations
TL;DR: A novel numerical approach for the a priori evaluation of the roll-over shape (ROS) of a prosthetic foot for application in its systematic design and development is introduced.
Abstract: Prosthetic feet have generally been designed experimentally by adopting a trial-and-error technique. The objective of this research is to introduce a novel numerical approach for the a priori evaluation of the roll-over shape (ROS) of a prosthetic foot for application in its systematic design and development. The ROS was achieved numerically by employing a non-linear finite element model incorporating the augmented Lagrangian and multi-point constraint contact formulations, a hyperelastic material model and a higher-order strain definition. The Ottobock Solid Ankle Cushion Heel (SACH) foot was chosen to experimentally validate the numerical model. The geometry of the foot was evaluated from optical scans, and the material properties were obtained from uniaxial tensile, shear and volumetric compression tests. A new setup was designed for an improved experimental determination of the ROS, with the inclusion of an extended moment arm and variable loading. Error analysis of the radius of curvature of the ROS between the numerical and experimental results showed the percentage error to be 7.52%, thereby establishing the validity of the model. A numerical design model of this kind can be utilised to vary the input design parameters to arrive at a prosthetic foot with specified performance characteristics effectively and economically.
5 citations
01 Jan 2010
TL;DR: This contribution presents two advances in the formulation of discontinuous approximations in finite elements by writing the strain field as a non-local weighted average of the compatible strain field, so that the usual subdivision into integration cells is not required and an isoparametric mapping is not needed.
Abstract: This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal domains [1]. When an element is split into two subdomains by a piecewise continuous discontinuity, each of these polygonal domains is mapped onto a unit disk on which cubature rules are utilized. This suppresses the need for the usual two-level isoparametric mapping. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the surface of the finite elements is transformed into boundary integration, so that the usual subdivision into integration cells is not required, an isoparametric mapping is not needed and the derivatives of the shape (enrichment) functions do not need to be computed. Results in fracture mechanics and composite materials are presented and both methods are compared in terms of accuracy and simplicity. The interested reader is referred to [1,6,13] for more details and should contact the authors to receive a version of the MATLAB codes used to obtain the results herein.
4 citations
TL;DR: A virtual element method for the time-dependent Stokes equation is presented by employing a mixed formulation involving the velocity and the pressure as primitive variables and the optimal order of convergence is estimated.
Abstract: In this paper, we present a virtual element method for the time-dependent Stokes equation by employing a mixed formulation involving the velocity and the pressure as primitive variables. The velocity is approximated using the $$H^1$$
conforming virtual element and the pressure is approximated by the discontinuous piecewise polynomial. In order to approximate the non-stationary part with optimal order of convergence, we need to compute the $$L^2$$
projection operator of the full order k. In view of this requirement, we modify the velocity space keeping the same dimension. The virtual space is discrete inf-sup stable for $$k \ge 2$$
and non-divergence free. We estimate the optimal order of convergence for the velocity and the pressure.
4 citations
TL;DR: The extension of the proposed forward Uncertainty Quantification (UQ) to take into account multiple independent random fields, followed by Polynomial Chaos Expansion (PCE) based sensitivity analysis is extended.
4 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