Virtual and Smoothed Finite Elements: IJNME paper online. Congratulations to Sundar!!

Natarajan, S.; Bordas, Stéphane; O’Higgins, R. M.; McCarthy, C. T.
in Composite Structures (2014), 107Virtual and smoothed finite elements: a connection and its application to polygonal/polyhedral finite element methods

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S Natarajan, S Bordas, ET Ooi – International Journal for Numerical Methods in Engineering, 2015

Summary We show both theoretically and numerically a connection between the smoothed (SFEM) and the virtual element method (VEM) and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the VEM, irrespective of the topology of the element as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements, where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element, while maintaining stability. For a similar number of degrees of freedom (dofs), the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the inline image in case of the conventional Polygonal FEM, whilst, it scales as inline image in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity.

Other papers by Sundararajan Natarajan

S Natarajan, S Bordas, D Roy Mahapatra, Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping, International Journal for Numerical Methods in Engineering, v80, 103-134, 2009. Preprint

S Natarajan, D Roy Mahapatra, S Bordas, Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework, International Journal for Numerical Methods in Engineering, v83, 269-294, 2010. Preprint

S Natarajan, ET Ooi, I Chiong, C Song, Convergence and accuracy of displacement based finite element formulations over arbitrary polygons: Laplace interpolants, strain smoothing and scaled boundary polygon formulation, Finite Elements in Analysis and Design, v85, 101-122, 2014.

S Natarajan, S Bordas, ET Ooi, On the connection between the cell-based smoothed finite element method and the virtual element method. Preprint

Supersonic flutter analysis of functionally graded material plates with cracks
Natarajan, Sundararajan; Manickam, Ganapathi; Bordas, Stéphane in Frontiers in Aerospace Engineering (2013), 2(2), 91–97

NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
Valizadeh, N; Natarajan, Sundarajan; González-Estrada, Octavio Andrés; Rabczuk, Timon; Bui, Tinh Quoc; Bordas, Stéphane in Composite Structures (2013), 99

An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae Cahill, L. M. A.; Natarajan, S.; Bordas, Stéphane; O’Higgins, R. M.; McCarthy, C. T. in Composite Structures (2014), 107

— Stephane Bordas