Sundararajan Natarajan

Sundararajan Natarajan
Indian Institute of Technology Madras | IIT Madras · Department of Mechanical Engineering

BE, PhD

About

286
Publications
63,752
Reads
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5,337
Citations
Citations since 2016
183 Research Items
4267 Citations
20162017201820192020202120220200400600800
20162017201820192020202120220200400600800
20162017201820192020202120220200400600800
20162017201820192020202120220200400600800
Introduction
Sundararajan Natarajan currently works at the Department of Mechanical Engineering, Indian Institute of Technology Madras.
Additional affiliations
August 2018 - present
Indian Institute of Technology Madras
Position
  • Professor (Associate)
August 2018 - present
Indian Institute of Technology Madras
Position
  • Professor (Associate)
September 2014 - July 2018
Indian Institute of Technology Madras
Position
  • Professor (Assistant)
Education
January 2009 - July 2011
Cardiff University
Field of study
  • Theoretical, Applied and Computational Mechanics
August 1995 - April 1999
Bharathiar University
Field of study
  • Mechanical Engineering

Publications

Publications (286)
Article
Full-text available
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed polygonal FEM with simple averaging technique and the scaled boundary polygon formulation. For th...
Article
Full-text available
In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does not require special numerical integration technique to compute the stiffness matrix and it improves the capab...
Article
This paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz–Christoffel mapping and a midpoint quadrature rule defined on this unit disk is used. This method eliminates the need for a two-level isoparametric mapping usually required. Moreover, th...
Article
Full-text available
In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify th...
Article
Full-text available
The nonlinear formulation developed based on von Karman's assumptions is employed to study the free vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction. The material is assumed t...
Chapter
We present the details of the implementation of the Virtual Element Method (VEM) for nonlinear elliptic and parabolic problems, over polygonal meshes. The VEM implementation of a nonlinear problem does not follow the traditional way of implementation of the nonlinear problems as done in finite element/finite volume or finite difference methods. To...
Article
Full-text available
In this work, we propose a new n+1 integration scheme over arbitrary polygonal elements based on centroid approximation and Richardson extrapolation scheme. For the purpose of numerical integration, the polygonal element is divided into quadrilateral subcells by connecting the centroid of the polygon with the mid-point of the edges. The bilinear fo...
Article
Full-text available
In this paper, we analyse the virtual element method for the quasi-linear convection-diffusion-reaction equation. The most important part in the analysis is the proof of existence and uniqueness of the branch of solution of the discrete problem. We extend the explicit analysis given by Lube (Numer. Math. 61, 335-357, 1992) for the finite element di...
Article
Due to the hierarchical structure, fibre reinforced polymer composites exhibits randomness at multiple scales, for example, the constituent material properties and the layer thickness could be random at micro and macroscale, respectively. In addition, some of these uncertainties may not have sufficient probability information to be precisely descri...
Article
The objective of this work is to study dynamic crack propagation in brittle materials under time-dependent loading conditions by using the recently developed adaptive isogeometric phase-field approach. The current approach owns several ingredients including the advantages of the phase-field method (PFM), which can be used to model complex crack mor...
Article
Full-text available
Super duplex stainless steel (SDSS) exhibits poor machinability due to its high mechanical strength and low thermal conductivity. The strong thermal gradient in the vicinity of the cutting zone during machining generates tensile residual stresses affecting the service life of a component. This necessitates the need for the development of predictive...
Article
The bending response of laminated composite sandwich structures developed for aircraft flaps is analyzed, in two parts. In the first part, the carbon fiber reinforced plastic (CFRP) and Aluminium 6061 based single-sided trapezoidal corrugated core sandwich panels are considered. The developed design is observed to withstand higher loads and exhibit...
Article
Full-text available
In this paper, an adaptive phase-field approach is proposed for three-dimensional fracture modeling in brittle materials. The scaled boundary finite element method (SBFEM) is used to solve the phase-field and elasticity equations in a staggered scheme. This is motivated by the ability of the SBFEM to handle polyhedral elements with hanging nodes st...
Article
Full-text available
Based on the error indicator computed from the scaled boundary equations, a quadtree based adaptive phase field method is proposed for dynamic brittle fracture problems in isotropic material using the scaled boundary finite element method (SBFEM). The use of SBFEM alleviates the need for additional: (a) constraints to handle hanging nodes resulting...
Article
Full-text available
In this paper, the cell-based smoothed finite element method (CS-FEM) is proposed for solving boundary value problems of gradient elasticity in two and three dimensions. The salient features of the CS-FEM are: it does not require an explicit form of the shape functions and alleviates the need for iso-parametric mapping. The main idea is to sub- div...
Article
In this work, a phase field cohesive zone model (PFCZM) combined with the cell-based smoothed finite element method (CSFEM) is presented to investigate the quasi-brittle fracture behaviour of concrete at mesoscale. An automatic quadtree decomposition technique is employed to discretise the CT image-based meso-structures including aggregates, mortar...
Article
The paper presents a novel approach for multi-frequency acoustic topology optimization of sound-absorption materials. In this work, the isogeometric boundary element method based on subdivision surfaces is used to solve Helmholtz equations defined in infinite domains. To avoid time-consuming frequency sweep, we adopt series expansion method to deco...
Chapter
The extended finite element method (XFEM) combined with a meta-heuristic optimization algorithm namely Quantum Particle Swarm Optimization (QPSO) is proposed in this paper for the identification of crack parameters (crack position) in plate structures. The XFEM is employed to solve the forward problem of strain estimation in a cracked plate due to...
Article
Full-text available
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 C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgr...
Article
In this work, a crack opening model is proposed to study the electrostatic tractions in the cracked semipermeable piezoelectric material. The extended finite element method (XFEM) is used in conjunction with six-fold electromechanical enrichment functions. The electric displacement intensity factor (EDIF) is evaluated in the presence of a dielectri...
Article
Full-text available
In this paper, an analytical solution for smart laminated composite and functionally graded material plates with and without through-thickness porosity is presented. The kinematics of the deformation in smart structures is modelled through the newly proposed five non-polynomial higher-order shear deformation theories. The relative performance and a...
Article
In this article, we consider the discretization of nonlocal coupled parabolic problem within the framework of the virtual element method. The presence of nonlocal coefficients not only makes the computation of the Jacobian more expensive in Newton's method, but also destroys the sparsity of the Jacobian. In order to resolve this problem, an equival...
Article
In this study, we present a displacement based polygonal finite element method for compressible and nearly-incompressible elastic solids undergoing large deformations in two dimensions. This is achieved by projecting the dilatation strain onto the linear approximation space, within the framework of volume averaged nodal projection method. To reduce...
Preprint
Full-text available
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, $k\ge2$, to approximate the model problem numerically. We employ VEM to discretize the space variable and ful...
Article
The scaled boundary finite element method is extended to model fracture in functionally graded materials (FGM) under coupled thermo-mechanical loads. The governing equations of coupled thermo-mechanical equilibrium are discretized using scaled boundary shape functions enriched with the thermal load terms. The material gradient is modeled as a serie...
Article
In the recent years, the phase field method (PFM) has gained considerably attention to model fracture process. This is because, in a single framework, the method allows to model crack nucleation, growth, coalescence and branching. In addition, existing FE codes can be used with minimal modifications. However, one of the major limitations of the PFM...
Article
The polygonal finite element method (PFEM) is proposed as a fast and accurate technique to simulate the impedance spectroscopy (IS) of polycrystalline materials. While conventional finite element method (FEM) requires explicit meshing of the grains and grain boundaries, in PFEM each region can be treated as an element. We demonstrate that the numbe...
Article
This work proposes an experimentally validated numerical approach for a systematic a priori evaluation of the energy storage and stress-strain characteristics of a prosthetic foot during the stance phase of walking. Boundary conditions replicating the rocker based inverted pendulum model were incorporated. The mechanically complex Ottobock Solid An...
Article
This paper develops the scaled boundary finite element method to analyze fracture of functionally graded magneto-electro-elastic materials. Polygon meshes are employed to discretize the domain. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required to calculate the intensity factors. When the mater...
Article
This paper aims at presenting a hybrid computational strategy and its detailed implementation for simulation of crack propagation problems in three-dimensional (3D) solids. The key idea of the hybrid approach lies in the combination of extended finite element method (XFEM) and bond-based peridynamics (PD), which takes excellent features of the high...
Article
This paper presents a discrete shear quadrilateral (DSQ) element to study the static bending, free vibration, and buckling analysis of functionally graded material plate structures. The effective properties of the FGM plate are computed using the rule of mixtures. The plate kinematics is based on Resinner-Mindlin plate theory with discrete shear co...
Article
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, 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 accur...
Article
Isogeometric Analysis (IGA) provides an alternative to Lagrange based finite element methods by representing the geometry and field with the same Non-Uniform Rational B-Splines (NURBS) shape functions within a weak Galerkin formulation. IGA has proven to be highly efficient in solving the Helmholtz equation, due to the ease with which the order and...
Article
Full-text available
Over the last several decades, the Finite Element Method (FEM) has emerged as the numerical approach method of choice for the solution of problems in solid mechanics. Part of the reason for the success of FEM is that it provides a unified framework for discretizing even complex differential equations. However, despite this overall unification, FEM...
Article
This paper presents a non-intrusive scaled boundary finite element method to consider multiple input uncertainties, viz., material and geometry. The types of geometric uncer- tainties considered include the shape and size of inclusions. The inclusions are implicitly defined, and a robust framework is presented to treat the interfaces, which does no...
Article
Delamination and cracking of matrix/fiber is a common failure phenomena reported in fiber reinforced compos- ite. As complex stress states develop in laminated structures, they are prone to fractures. Therefore, designs with large damage tolerance are currently implemented in most of the industrial sectors. This can be achieved by designing the com...
Article
We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual element method is based on the lowest-order virtual element space that contains the subspace of the linear polynomials...
Preprint
Full-text available
Compared to conventional projection-based model-order-reduction, its neural-network acceleration has the advantage that the online simulations are equation-free, meaning that no system of equations needs to be solved iteratively. Consequently, no stiffness matrix needs to be constructed and the stress update needs to be computed only once per incre...
Article
Full-text available
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 analysed. Using suitable projection operators, the bilinear and trilinear terms are discretised by only using the proposed degrees of freedom associated with the virtual space. Under certai...
Article
The scatter in the fatigue behavior of duplex microstructure titanium alloys occurs due to microstructural randomness. The presence of two phases in titanium alloy microstructure also contributes to the scatter in fatigue life data. In the literature, several mathematical frameworks have been developed to consider the effect of microstructural rand...
Article
In the present work, a novel load-controlled iteration scheme within the framework of extended finite element method (XFEM) is proposed to model the semipermeable crack in a piezoelectric material. To capture the stress and electric displacement singularity at the crack tip, the electromechanical 6-fold enrichment functions are used. The domain for...
Article
Full-text available
This work presents a framework to study the quasi-static brittle fracture in functionally graded materials with random material properties using a non-intrusive phase field method. The model accounts for variation in the material and fracture properties. Further, the effective Young's modulus, the gradient index and the fracture properties of the c...
Article
Full-text available
In this study, three variants of strain smoothing technique, viz., the cell-based, edge-based and the node-based smoothed finite element method are employed for structural topology optimization. The salient features of the strain smoothing technique are: (a) does not require an explicit form of shape functions and (b) less sensitive to mesh distort...
Article
Performance evaluation of prosthetic feet during its design is typically performed experimentally, which may be time and cost intensive. This work presents a first-of-its-kind application of a numerical procedure for the a priori determination of various stance phase biomechanical parameters of a prosthetic foot, such as its roll-over characteristi...
Article
A recovery-based error indicator developed to evaluate the quality of polygonal finite element approximations is presented in this paper. Generalizations of the finite element method to arbitrary polygonal meshes have been increasingly investigated in the last years, as they provide flexibility in meshing and improve solution accuracy. As any numer...
Preprint
Full-text available
We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual element method is based on the lowest-order virtual element space that contains the subspace of the linear polynomials...
Article
Full-text available
Amongst the available methods to model fracture processes, the phase field approach has proved to be efficient and has received extensive attention. However, the approach is computationally demanding as it requires a very high resolution, both in space and time to resolve the fracture characteristics. In this paper, a novel adaptive phase field met...
Article
In this work, we propose to replace the conventional flat stainless steel gasket in flanged bolted joints used in seawater piping with an O-ring polymer gasket to provide a leak-proof joint under bolt preload. Modeled as hyperelastic material, the polymer gasket undergoes large deformation when sandwiched between the pipe flanges. To alleviate the...
Article
Full-text available
In this paper, an adaptive phase field scaled boundary finite element method for fracture in functionally graded material is presented. The model accounts for spatial variation in the material and fracture properties. The quadtree decomposition is adopted for refinement and the refinement is based on an error indicator evaluated directly from the s...
Article
Full-text available
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 app...
Article
In this paper, we propose a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomegeneous media. The salient features of the proposed work are: (a) interfaces can be implicitly defined and need not conform to the background mesh; (b) Dirichlet boundary co...
Chapter
In this chapter, by employing a basis B-splines based finite element method, the natural frequency, critical buckling load and critical aerodynamic pressure of tow-steered composite laminate is numerically studied. The distinguishing feature of tow-steered composites when compared to conventional laminated composites is that in the former, a spatia...
Chapter
The phase field approach for simulating fracture has gained significant attention in recent years due to the following salient features: 1) the scalar damage variable is implicitly used to describe the discontinuous surface; 2) the crack initiation and subsequent propagation and branching / coalescence are handled with minimal complexity and 3) can...
Chapter
In this chapter, by employing a basis B-splines based finite element method, the natural frequency, critical buckling load and critical aerodynamic pressure of tow-steered composite laminate is numerically studied. The distinguishing feature of tow-steered composites when compared to conventional laminated composites is that in the former, a spatia...
Article
Full-text available
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement. The proposed approach is capable of capturing the fracture process with a localized mesh refin...
Article
Full-text available
The paper aims to evaluate the performance of the Lagrange-based Finite Element Method and the Non Uniform Rational B-Splines Isogeometric Analysis of time-harmonic acoustic exterior scattering problems using high-order local absorbing boundary conditions, in particular based on the Karp's and Wilcox's farfield expansions. The analysis of accuracy...
Article
In this paper, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range in two and three dimensions. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not requ...
Article
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 me...
Presentation
Full-text available
Abstract of the online presentation in the World Congress of Computational Mechanics (WCCM), covering the topic “Isogeometric shape optimization of piezoelectric energy harvesters.”
Article
Full-text available
This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severe...
Article
Problems involving material interfaces are challenging, owing to the cumbersome requirements in meshing such as a fine matching mesh on both sides of the interface. Often one does not require very fine meshes on either side of the interface owing to different geometric and material properties. If the interface meshes are finer on either side, the d...
Article
Full-text available
The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assumed strain technique based on Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct evaluation from the basis functions and the displacement fields. The und...