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.

Design of a Biomimetic SACH Foot: An Experimentally Verified Finite Element Approach

Abstract: The Solid Ankle Cushioned Heel (SACH) foot is a commonly prescribed prosthetic foot for the rehabilitation of lower limb amputees. From the viewpoint of its biomechanical performance, the foot is known to cause drop-off effect and asymmetry in amputee gait. Therefore, the objective of this work is to improvise the effective foot length ratio (EFLR) and the progression of the centre of pressure (CoP) of the SACH foot by providing a novel design approach that utilizes finite element analysis. Boundary conditions employed for evaluating the roll-over characteristics of prosthetic feet were numerically incorporated in this work. The non-linear mechanical behavior of the foot was included with the incorporation of large deformation, a hyperelastic material model and the Augmented Lagrangian contact formulation. Outcomes from the simulations were experimentally verified using an inverted pendulum-like apparatus, thereby substantiating the numerical approach. The design process of the SACH foot involved the modification of the elastic modulus of its components for enhancing the parameters of interest. Results obtained presented a 5.07% increase in the EFLR and a 9.29% increase in the anteroposterior progression of the CoP, which may improve amputee stability. The design solution presented may support the large user base of the SACH foot towards achieving enhanced gait characteristics during ambulation. Moreover, this work successfully demonstrates a novel design procedure for a prosthetic foot through an effective numerical implementation.

Linear flutter analysis of functionally graded panels using cell based smoothed finite element method and discrete shear gap technique

Abstract: In this paper, a cell-based smoothed finite element method wi th discrete shear gap technique for triangular elements is employed to study the linear flutter characteristic s of functionally graded material (FGM) flat panels. The influence of thermal environment, the presence of a centr ally located circular cutout and the aerodynamic damping on the supersonic flutter characteristics of flat FGM panels is also investigated. The structural formulation is based on the first-order shear deformation theor y and the material properties are assumed to be temperature dependent and graded only in the thickness direction according to power law distribution in terms of the volume fraction of its constituent materials. The aer odynamic force is evaluated by considering the first order high mach number approximation to linear potential flo w theory. The formulation includes transverse shear deformation and in-plane and rotary inertia effects. The influence of the plate thickness, aspect ratio, boundary conditions, material gradient index, temperature dependent material properties, damping, cutout size, skewness of the plate and boundary conditions on the critical aerodynamic pressure is numerically studied.

Analysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method

Abstract: In this paper, a cell based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first order shear deformation theory and the shear locking is suppressed by a discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence the gradient index, the plate aspect ratio, skewness of the plate and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied.

Bounds of mechanical properties of fibre reinforced polymer composites with hybrid random and interval uncertainties

Abstract: 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 described as random variables, and they are treated as interval variables. This study, proposes a novel framework to estimate the boundary of mechanical properties of fibre reinforced polymer composites with hybrid and internal uncertainties. Within this framework, the random and interval uncertainties are expressed in terms of Hermite and Chebyshev polynomials, respectively, within the PCE-based surrogate model. By doing so, the multiscale analysis is embedded in the hybrid surrogate model to realize the multiscale random-interval uncertainty analysis. Numerical examples are carried out to demonstrate the feasibility of the proposed method, and results show that this method can accurately obtain the upper and lower bounds of structural responses, e.g. failure probability, of FRP composite structures. • Bounds of mechanical properties with uncertainties for composite were determined. • Both aleatory and epistemic uncertainties at micro- and macro-scales are considered. • Uncertainty quantification is carried out by surrogate model based on PCE method.

Continuum modelling of stress diffusion interactions in an elastoplastic medium in the presence of geometric discontinuity.

Abstract: Chemo-mechanical coupled systems have been a subject of interest for many decades now. Previous attempts to solve such models have mainly focused on elastic materials without taking into account the plastic deformation beyond yield, thus causing inaccuracies in failure calculations. This paper aims to study the effect of stress-diffusion interactions in an elastoplastic material using a coupled chemo-mechanical system. The induced stress is dependent on the local concentration in a one way coupled system, and vice versa in a two way coupled system. The time-dependent transient coupled system is solved using a finite element formulation in an open-source finite element solver FEniCS. This paper attempts to computationally study the interaction of deformation and diffusion and its effect on the localization of plastic strain. We investigate the role of geometric discontinuities in scenarios involving diffusing species, namely, a plate with a notch/hole/void and particle with a void/hole/core. We also study the effect of stress concentrations and plastic yielding on the diffusion-deformation. The developed code can be from this https URL

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.

The Hitchhiker's Guide to the Virtual Element 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.