CMES-Vol. 105, No. 2, 2015

Open Access

ARTICLE

A Meshless LBIE/LRBF Method for Solving the Nonlinear Fisher Equation: Application to Bone Healing
K. N. Grivas¹, M. G. Vavva¹, E. J. Sellountos², D. I. Fotiadis³, D. Polyzos^1,4
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 87-122, 2015, DOI:10.3970/cmes.2015.105.087
Abstract A simple Local Boundary Integral Equation (LBIE) method for solving the Fisher nonlinear transient diffusion equation in two dimensions (2D) is reported. The method utilizes, for its meshless implementation, randomly distributed nodal points in the interior domain and nodal points corresponding to a Boundary Element Method (BEM) mesh, at the global boundary. The interpolation of the interior and boundary potentials is accomplished using a Local Radial Basis Functions (LRBF) scheme. At the nodes of global boundary the potentials and their fluxes are treated as independent variables. On the local boundaries, potential fluxes are avoided by More >

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Estimation of Isotropic Hyperelasticity Constitutive Models to Approximate the Atomistic Simulation Data for Aluminium and Tungsten Monocrystals
Marcin Maździarz¹, Marcin Gajewski²
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 123-150, 2015, DOI:10.3970/cmes.2015.105.123
Abstract In this paper, the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined. The article discusses some physical, mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful. A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed, and an algorithm for parametrisation is discussed. The proposed models with optimised parameters are superior to those used in non-linear More >

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A Semi-analytical Method for Vibrational and Buckling Analysis of Functionally Graded Nanobeams Considering the Physical Neutral Axis Position
Farzad Ebrahimi^1,2, Erfan Salari¹
CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 151-181, 2015, DOI:10.3970/cmes.2015.105.151
Abstract In this paper, a semi-analytical method is presented for free vibration and buckling analysis of functionally graded (FG) size-dependent nanobeams based on the physical neutral axis position. It is the first time that a semi-analytical differential transform method (DTM) solution is developed for the FG nanobeams vibration and buckling analysis. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form. The physical neutral axis position for mentioned FG nanobeams is determined. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The… More >

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