Showing papers by "Sundararajan Natarajan published in 2012"

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

Abstract: An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth+singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain precise error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.

Free flexural vibration of functionally graded size-dependent nanoplates

Abstract: In this paper, the linear free flexural vibration behaviour of functionally graded (FG) size-dependent nanoplates are investigated using the finite element method. The field variables are approximated by non-uniform rational B-splines. The size-dependent FG nanoplate is investigated by using 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 FG nanoplate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is tested 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 FG nanoplate.

Supersonic flutter analysis of thin cracked functionally graded material plates

Abstract: In this paper, the flutter behaviour of simply supported square functionally graded material plates immersed in a supersonic flow is studied. An enriched 4-noded quadrilateral element based on field consistency approach is used for this study and the crack is modelled independent of the underlying mesh. The material properties are assumed to be temperature dependent and graded only in the thickness direction. The effective material properties are estimated using the rule of mixtures. The formulation is based on the first order shear deformation theory and the shear correction factors are evaluated employing the energy equivalence principle. The influence of the crack length, the crack orientation, the flow angle and the gradient index on the aerodynamic pressure and the frequency are numerically studied. The results obtained here reveal that the critical frequency and the critical pressure decreases with increase in crack length and it is minimum when the crack is aligned to the flow angle.

Representation of singular fields without asymptotic enrichment in the extended finite element method

Abstract: 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 capability of the XFEM to model cracks in homogeneous and/or heterogeneous materials without a priori knowledge of the asymptotic solutions. A heaviside enrichment is used to represent the jump across the discontinuity surface. We call the method as the extended scaled boundary finite element method (xSBFEM). Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics show that the proposed method yields accurate results with improved condition number. A simple MATLAB code is annexed to compute the terms in the stiffness matrix, which can easily be integrated in any existing FEM/XFEM code.

Strategies to Build Viable Community Seed System in Dryland Ecosystems for Sustainable Seed and Food Security in India

Abstract: To make available and affordable good quality seed at the right time requires a well functioning seed supply system This in turn will help to ensure seed security and enhancing productivity in dryland areas Given the critical role that improved varieties can potentially play in increasing the production of conventional cropping systems, developing an integrated and effective seed system capable of generating and delivering improved seed varieties in a cost-effective ways is a challenge Farmers' seed systems in agrarian communities have stood the test oftime to enable evolution of modern agriculture Thus the informal seed sector has ensured conservation of agro-bio-diyersity, at the gene, ecosystem, and farmer levels to ensure food security A relatively recent analysis has led to an understanding of the crucial role that women have played in sustaining the informal seed sector, and more widely, in ensuring food security However, this sector is solely dependent on local resources and inputs, and seed supply is highly vulnerable to disaster and socio-political disruptions Sowing the seeds of innovation therefore assumes great urgency if one is to strengthen local seed systems While the hybrid seed industry led by the private sector in formal seed systems has focused on profit-making species and crops, the informal sector has concentrated on those crops and seed systems which underpin local food production, mainly those predominantly self pollinating and open pollinated Given this scenario, national seed policies must devote more effort to sustaining and strengthening the informal seed sector Most of the international support to strengthening seed systems focuses on the formal seed sector; the time has come for matching support to the informal sector

Smoothed finite element method for two-dimensional elasto-plasticity

Abstract: This communication shows how the smoothed finite element method (SFEM) very recently proposed by G.R. Liu [14] can be extended to elasto-plasticity. The SFEM results are in excellent agreement with the finite element (FEM) and analytical results. For the examples treated, the method is quite insensitive to mesh distortion and volumetric locking. Moreover, the SFEM yields more compliant load-displacement curves compared to the standard, displacement based FE method, as expected from the theoretical developments recently published in [4], [3] and [6].

On the application of polynomial and NURBS functions for nonlocal response of low dimensional structures

Abstract: In this paper, the axial vibration of cracked beams, the free flexural vibrations of nanobeams and plates based on Timoshenko beam theory and first-order shear deformable plate theory, respectively, using Eringen’s nonlocal elasticity theory is numerically studied. The field variable is approximated by Lagrange polynomials and non-uniform rational B-splines. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the natural frequency is numerically studied. The influence of a crack on axial vibration is also studied. The results obtained from this study are found to be in good agreement with those reported in the literature.