Sundararajan Natarajan

Bio: Sundararajan Natarajan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topic(s): Finite element method & Extended finite element method. The author has an hindex of 34, co-authored 181 publication(s) receiving 4087 citation(s). Previous affiliations of Sundararajan Natarajan include GE Aviation & Bauhaus University, Weimar.

Strain smoothing in FEM and XFEM

Abstract: We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B.

NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter

Abstract: In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori–Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

Size-dependent free flexural vibration behavior of functionally graded nanoplates

Abstract: In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method The field variables are approximated by non-uniform rational B-splines The nonlocal constitutive relation is based on Eringen’s differential form of nonlocal elasticity theory The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori–Tanaka homogenization scheme The accuracy of the present formulation is demonstrated considering the problems for which solutions are available A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length

Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping

Abstract: This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

Abstract: This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

American Society for Testing and Materials

Abstract: The American Society for Testing and Materials (ASTM) is an independent organization devoted to the development of standards.

The extended/generalized finite element method: An overview of the method and its applications

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.

Review: Meshless methods: A review and computer implementation aspects

Abstract: The aim of 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 our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enrichment, point collocation methods, several boundary condition enforcement schemes and corresponding test cases. Several one and two-dimensional examples in elastostatics are given including weak and strong discontinuities and testing different ways of enforcing essential boundary conditions.

Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review

Abstract: Research activities related to functionally graded materials (FGMs) have increased rapidly in recent years. The superlative properties of carbon nanotubes, i.e. high strength, high stiffness, high aspect ratio and low density have made them an excellent reinforcement for composite materials. Inspired by the concept of FGMs, the functionally graded (FG) pattern of reinforcement has been applied for functionally graded carbon nanotube reinforced composite (FG-CNTRC) materials. This paper attempts to identify and highlight topics relevant to FG-CNTRC and reviews the recent research works that have been reported in these topics. The present review includes: (i) a brief introduction of carbon nanotube reinforced composite (CNTRC) material; (ii) a review of mechanical analysis of FG-CNTRC; and (iii) a detailed discussion on the recent advances of FG-CNTRC and its prospect.

Nonlinear Finite Elements For Continua And Structures

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