RaviS Nanjundiah¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 1-24, 2008, DOI:10.3970/cmes.2008.027.001

Abstract In this paper, application of high performance computing to climate modelling with specific reference to global General Circulation Models (GCM) is discussed. Methods of parallelization of global atmospheric models based on their numerical schemes is presented. It is seen that there is an interesting co-evolution of computer architecture and the type of numerical schemes used in general circulation models. A detailed survey of the Indian HPC scenario for meteorological computing is presented. Innovative and pioneering aspects of Indian efforts are highlighted. More >

G.F. Karlis¹, S.V. Tsinopoulos², D. Polyzos³, D.E. Beskos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 189-208, 2008, DOI:10.3970/cmes.2008.026.189

Abstract A boundary element method, suitable for solving two and three dimensional gradient elastic fracture mechanics problems under static loading, is presented. A simple gradient elastic theory (a simplied version of Mindlin's Form-II general theory of gradient elasticity) is employed and the static gradient elastic fundamental solution is used to construct the boundary integral representation of the problem with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well-posed problem. Surface More >

Thi D. Dang¹, Bhavani V. Sankar²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 169-188, 2008, DOI:10.3970/cmes.2008.026.169

Abstract In this paper the meshless local Petrov-Galerkin (MLPG) method is used in the micromechanical analysis of a unidirectional fiber composite. The methods have been extended to include shear loadings, thus permitting a more complete micromechanical analysis of the composite subjected to combined loading states. The MLPG formulation is presented for the analysis of the representative volume element (RVE) of the periodic composite containing material discontinuities. Periodic boundary conditions are imposed between opposite faces of the RVE. The treatment of periodic boundary conditions in the MLPG method is handled by using the multipoint constraint technique. Examples More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 157-168, 2008, DOI:10.3970/cmes.2008.026.157

Abstract For the Sturm-Liouville eigenvalues problem we construct a very effective Lie-group shooting method (LGSM) to search the eigenvalues, and when eigenvalue is determined we can also search a missing left-boundary condition of the slope through a weighting factor r ∈ (0,1). Hence, the eigenvalues and eigenfunctions can be calculated with a better accuracy. Because a closed-form formula is derived to calculate unknown slope in terms of λ for the estimation of eigenvalues, the present method is easy to implement and has a low computational cost. Similarly by applying the LGSM to find a corresponding eigenfunction in More >

Z. Chen^1,2, Y. Gan¹, J.K. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 123-138, 2008, DOI:10.3970/cmes.2008.026.123

Abstract A coupled thermo-mechanical constitutive model with decohesion is proposed to simulate the material failure evolution due to localized heating. A discontinuous bifurcation analysis is performed based on a thermoviscoplasticity relation to identify the transition from continuous to discontinuous failure modes as well as the orientation of the discontinuous failure. The thermo-mechanical model is then implemented within the framework of the Material Point Method (MPM) so that the different gradient and divergence operators in the governing differential equations could be discretized in a single computational domain and that continuous remeshing is not required with the evolution More >

Kai Wang¹, Shenjie Zhou^1,2, Zhifeng Nie¹, Shengli Kong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 107-122, 2008, DOI:10.3970/cmes.2008.026.107

Abstract The natural neighbour Petrov-Galerkin method (NNPG) is one of the special cases of the generalized meshless local Petrov-Galerkin method (MLPG). This paper demonstrates the NNPG can be successfully used in design sensitivity analysis in 2D elasticity. The design sensitivity analysis method based on the local weak form (DSA-LWF) in the NNPG context is proposed. In the DSA-LWF, the local weak form of governing equation is directly differentiated with respect to design variables and discretized with NNPG to obtain the sensitivities of structural responds. The calculation of derivatives of shape functions with respect to design variables More >

Y. Nishidate¹, G. P. Nikishkov^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 91-106, 2008, DOI:10.3970/cmes.2008.026.091

Abstract Atomic-scale finite element procedure for modeling of self-positioning nanostructures is developed. Our variant of the atomic-scale finite element method is based on a meshless approach and on the Tersoff interatomic potential function. The developed algorithm is used for determination of equilibrium configuration of atoms after nanostructure self-positioning. Dependency of the curvature radius of nanostructures on their thickness is investigated. It is found that for thin nanostructures the curvature radius is considerably smaller than predicted by continuum mechanics equations. Curvature radius variation with varying orientation of crystallographic axes is also modeled and results are compared to More >

Zdenko Tonković¹, Jurica Sorić^1,2, Ivica Skozrit¹

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 75-90, 2008, DOI:10.3970/cmes.2008.026.075

Abstract An efficient numerical algorithm for modeling of cyclic elastoplastic deformation of shell structures is derived. The constitutive model includes highly nonlinear multi-component forms of kinematic and isotropic hardening functions in conjunction with von Mises yield criterion. Therein, the closest point projection algorithm employing the Reissner-Mindlin type kinematic model, completely formulated in tensor notation, is applied. A consistent elastoplastic tangent modulus ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite shell element, which is capable of geometrical nonlinearities including finite rotations. Numerical examples, More >

Shu Li¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.1, pp. 61-74, 2008, DOI:10.3970/cmes.2008.026.061

Abstract The Meshless Local Petrov-Galerkin (MLPG) "mixed collocation'' method is applied to the problem of topology-optimization of elastic structures. In this paper, the topic of compliance minimization of elastic structures is pursued, and nodal design variables which represent nodal volume fractions at discretized nodes are adopted. A so-called nodal sensitivity filter is employed, to prevent the phenomenon of checkerboarding in numerical solutions to the topology-optimization problems. The example results presented in the paper demonstrate the suitability and versatility of the MLPG "mixed collocation'' method, in implementing structural topology-optimization. More >

Amit Shaw¹, B. Banerjee¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.1, pp. 31-60, 2008, DOI:10.3970/cmes.2008.026.031

Abstract A generalization of a NURBS based parametric mesh-free method (NPMM), recently proposed by Shaw and Roy (2008), is considered. A key feature of this parametric formulation is a geometric map that provides a local bijection between the physical domain and a rectangular parametric domain. This enables constructions of shape functions and their derivatives over the parametric domain whilst satisfying polynomial reproduction and interpolation properties over the (non-rectangular) physical domain. Hence the NPMM enables higher-dimensional B-spline based functional approximations over non-rectangular domains even as the NURBS basis functions are constructed via the usual tensor products of… More >