L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 69-118, 2011, DOI:10.3970/cmes.2011.081.069

Abstract In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed fields at the boundary and… More >

M.A. Argenta¹, A.P. Gebert², E.S. Filho³, B.A. Felizari⁴, M.B. Hecke⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.3&4, pp. 159-182, 2011, DOI:10.3970/cmes.2011.079.159

Abstract Various methods in the literature proposesequations to calculate the stiffness as a function of density of bone tissue such as apparent density and ash density among others[Helgason, Perilli, Schileo, Taddei, Brynjolfsson and Viceconti, 2008]. Other ones present a value of an equivalent elasticity modulus, obtained by statistical adjustments of curves generated through mechanical compression tests over various specimens[Chevalier, Pahr, Allmer, Charlebois and Zysset, 2007; Cuppone, Seedhom, Berry and Ostell, 2004]. Bone tissue is a material withdifferent behaviors according to the scale of observation. It has a complex composite hierarchical structure, which is responsible for assign optimal mechanical properties. Its characteristics,… More >

K. Jayabal¹, A. Menzel^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 183-208, 2011, DOI:10.3970/cmes.2011.073.183

Abstract Naturally evolving Voronoi discretisation of two-dimensional plane domains renders representative microstructures that turn out to be useful for the modelling and simulation of polycrystalline materials. Hybrid finite element approaches are employed on such polygonal discretisations to solve, for instance, mechanical and electromechanical problems within a finite element context. In view of solving mechanical problems, varying order of polynomial functions are suggested in the literature to sufficiently approximate stresses within the polygonal finite elements. These are, in addition to the order of the approximation functions for the displacements, characterised by the number of edges in the polygonal elements. It appears, as… More >

A. Idesman ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 111-148, 2011, DOI:10.3970/cmes.2011.071.111

Abstract The paper deals with the following issues of existing time-integration methods for a semi-discrete system of elastodynamics equations: a) the quantification and the suppression of spurious high frequencies; b) the selection of the amount of numerical dissipation for a time-integration method; and c) accurate time integration of low modes. The finite element method used in the paper or other methods can be applied for the space discretization. A new two-stage time-integration procedure consisting of basic computations and the filtering stage is developed. For accurate integration of all frequencies, a time-integration method with zero (or small) numerical dissipation is applied for… More >

Marcin Maździarz¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 1-24, 2010, DOI:10.3970/cmes.2010.066.001

Abstract The paper presents unified approach to 3D isoparametric Lagrange brick, tetra, and prism finite elements. All shape functions, linear, quadratic and cubic, are depicted in one Cartesian orthogonal coordinate system x,y,z regardless of the type of element. This allows one to use a single transformation rule to calculate global derivatives and a second for integration. Proper numerical Gauss quadratures for these isoparametric elements in a unified approach are presented additionally. More >

K.P. Baxevanakis¹, A.E. Giannakopoulos²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 181-198, 2010, DOI:10.3970/cmes.2010.060.181

Abstract The present work gives a systematic and rigorous implementation of (edge type) circular Volterra dislocation loops in ordinary axisymmetric finite elements using the thermal analogue and the integral representation of dislocations through stresses. The accuracy of the proposed method is studied in problems where analytical solutions exist. The full fields are given for loop dislocations in isotropic and anisotropic crystals and the Peach-Koehler forces are calculated for loops approaching free surfaces and bimaterial interfaces. The results are expected to be very important in the analysis of plastic yield strength, giving quantitative results regarding the influence of grain boundaries, interstitial particles,… More >

A. Frangi¹, M. Pagani¹, U. Perego¹, R. Borsari²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.3, pp. 205-224, 2010, DOI:10.3970/cmes.2010.057.205

Abstract This paper is concerned with the finite element simulation of a thin membrane cutting by a sharp blade. Smeared crack finite element approaches appear to be unsuitable for this purpose, since very small elements would be required to conform to the sharp edge of the cutter. Furthermore, when the membrane material is very ductile, classical interface cohesive elements, where the cohesive forces are transmitted in the direction of the crack opening displacement, cannot correctly reproduce situations where the blade crosses the process zone. A simplified approach, based on the new concept of "directional" cohesive elements, is here proposed for a… More >

Ronan Madec¹, Dimitri Komatitsch^1,2, Julien Diaz³

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.2, pp. 163-190, 2009, DOI:10.3970/cmes.2009.049.163

Abstract When studying seismic wave propagation in fluid-solid models based on a numerical technique in the time domain with an explicit time scheme it is often of interest to resort to time substepping because the stability condition in the solid part of the medium can be more stringent than in the fluid. In such a case, one should enforce the conservation of energy along the fluid-solid interface in the time matching algorithm in order to ensure the accuracy and the stability of the time scheme. This is often not done in the available literature and approximate techniques that do not enforce… More >

Delfim Soares Jr.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 157-176, 2009, DOI:10.3970/cmes.2009.044.157

Abstract The numerical modelling of electromagnetic waves by finite element - boundary element coupling procedures is discussed here, taking into account time-domain approaches. In this study, the global model is divided into different sub-domains and each sub-domain is analysed independently and explicitly at each time-step of the analysis: the interaction between the different sub-domains of the global model is accomplished by interface procedures. A multi-level time-step algorithm is considered in order to improve the flexibility, accuracy and stability (especially when conditionally stable time-marching procedures are employed) of the coupled analysis. At the end of the paper, numerical examples are presented, illustrating… More >

F. Daghia¹, W. Hasan¹, L. Nobile¹, E. Viola^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.039.001

Abstract In this paper, a finite element model has been developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam was discretized into a number of finite elements having four degrees of freedom each. The effect of end springs was incorporated in order to identify the end constraints. \newline The procedure for identifying geometric and mechanical parameters as well as the end restraints of a beam on two-parameter elastic foundation is based on experimentally measured natural frequencies from dynamic tests on the structure itself. \newline An iterative statistical identification method, based on the… More >