References of "Natarajan, Sundarajan"
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See detailThe stable GFEM. Convergence, accuracy and Diffpack implementation
Alves Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

Presentation (2015, May 12)

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See detailNURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
Valizadeh, N; Natarajan, Sundarajan; González-Estrada, Octavio Andrés et al

in Composite Structures (2013), 99

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 ... [more ▼]

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. [less ▲]

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See detailStable extended finite element method: Convergence, Accuracy, Properties and Diffpack implementation
Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013)

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally ... [more ▼]

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally opposed approaches are attempting to simplify the CAD to Analysis pipeline: isogeometric methods on the one hand [1] aim at coupling the geometry and field approximations, whilst implicit boundary definition-based methods attempt to decouple them [3,4,5]. We examine in this paper one instance of the latter approach, and rely on partition of unity enrichment of the field variable to capture discontinuities along material interface or domain boundaries. We study in particular the stable generalized finite element method of Babuˇka and Banerjee [6] for higher order approximations in two and three dimensions and propose a generic implementation within the C++ library Diffpack from inuTech GmbH [7]. In a companion paper, the implementation of enrichment within Diffpack is presented in more detail. We will present results obtained with our 3D implementation of partition of unity enrichment within Diffpack. This implementation represents the interfaces through level-sets and palliates blending problems using various approaches. We study here the stabilisation approach proposed in [6] in more detail and pay particular attention to the global convergence rate of the approach and to the stability and the local flux converence close to the interfaces. [less ▲]

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