S. Tangaramvong¹, F. Tin-Loi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.3, pp. 217-256, 2009, DOI:10.3970/cmes.2009.042.217

Abstract Classical limit analysis is extended to include the effects of 2nd-order geometric and material nonlinearities, as well as the inclusion of limited ductility constraints. For the class of frame structures considered, the material constitutive model adopted can simultaneously accommodate the effects of combined axial and flexural force as well as local softening instability through the use of piecewise linearized yield surfaces. The main feature of the approach developed is to compute, in a single step, an upper bound to the maximum load. Corresponding displacements and stresses can be obtained as a by-product of the analysis. The problem is formulated as… More >

P. Bettini, E. Brusa, M. Munteanu, R. Specogna, F. Trevisan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 215-242, 2008, DOI:10.3970/cmes.2008.033.215

Abstract Electrostatic microactuator is a paradigm of MEMS. Cantilever and double clamped microbeams are often used in microswitches, microresonators and varactors. An efficient numerical prediction of their mechanical behaviour is affected by the nonlinearity of the electromechanical coupling. Sometimes an additional nonlinearity is due to the large displacement or to the axial-flexural coupling exhibited in bending. To overcome the computational limits of the available numerical methods two new formulations are here proposed and compared. Modifying the classical beam element in the Finite Element Method to allow the implementation of a \emph {Non incremental sequential approach} is firstly proposed. The so-called \emph… More >

L. Codecasa¹, R. Specogna², F. Trevisan³

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 129-144, 2008, DOI:10.3970/cmes.2008.031.129

Abstract In the paper we introduce a methodology to construct discrete constitutive matrices relating magnetic fluxes with magneto motive forces (reluctance matrix) and electro motive forces with currents (conductance matrix) needed for discretizing eddy current problems over hexahedral primal grids by means of the Finite Integration Technique (FIT) and the Cell Method (CM). We prove that, unlike the mass matrices of Finite Elements, the proposed matrices ensure both the stability and the consistency of the discrete equations introduced in FIT and CM. More >

C. K. Au¹

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.3, pp. 151-162, 2008, DOI:10.3970/cmes.2008.029.151

Abstract Ribbons may be used for the modeling of DNAs and proteins. The topology of a ribbon can be described by the linking number, while its geometry is represented by the writhe and the twist. These quantities are integrals and are related by the Cǎlugǎreanu's theorem from knot theory. This theorem also describes the relationship between the various conformations. The heart of the Cǎlugǎreanu's theorem rests in the Gauss Integral. Due to the large number of molecules, the topology and the geometry of a ribbon model can be very complicated. As a result, these integrals are commonly evaluated by numerical methods.… More >

D. Kourounis¹, L.N. Gergidis¹, A. Charalambopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.3, pp. 185-202, 2008, DOI:10.3970/cmes.2008.028.185

Abstract The sensitivity of analytical solutions of the direct acoustic scattering problem in prolate spheroidal geometry on the wavenumber and shape, is extensively investigated in this work. Using the well known Vekua transformation and the complete set of radiating "outwards'' eigensolutions of the Helmholtz equation, introduced in our previous work ([Charalambopoulos and Dassios(2002)], [Gergidis, Kourounis, Mavratzas, and Charalambopoulos (2007)]), the scattered field is expanded in terms of it, detouring so the standard spheroidal wave functions along with their inherent numerical deficiencies. An approach is employed for the determination of the expansion coefficients, which is optimal in the sense, that minimizes the… More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li¹, X. Zhao², T.T. Nguyen², G.Y. Sun¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.2, pp. 109-126, 2008, DOI:10.3970/cmes.2008.028.109

Abstract A smoothed finite element method (SFEM) is presented to analyze linear and geometrically nonlinear problems of plates and shells using bilinear quadrilateral elements. The formulation is based on the first order shear deformation theory. In the present SFEM, the elements are further divided into smoothing cells to perform strain smoothing operation, and the strain energy in each smoothing cell is expressed as an explicit form of the smoothed strain. The effect of the number of divisions of smoothing cells in elements is investigated in detail. It is found that using three smoothing cells for bending strain energy integration and one… More >

G. M. Kulikov¹, S. V. Plotnikova¹

CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.1, pp. 15-38, 2008, DOI:10.3970/cmes.2008.028.015

Abstract This paper presents a robust non-linear geometrically exact four-node solid-shell element based on the first-order seven-parameter equivalent single-layer theory, which permits us to utilize the 3D constitutive equations. The term "geometrically exact" reflects the fact that geometry of the reference surface is described by analytically given functions and displacement vectors are resolved in the reference surface frame. As fundamental shell unknowns six displacements of the outer surfaces and a transverse displacement of the midsurface are chosen. Such choice of displacements gives the possibility to derive strain-displacement relationships, which are invariant under arbitrarily large rigid-body shell motions in a convected curvilinear… 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 their one-dimensional counterparts. Nevertheless the… More >

A.P.S. Selvadurai¹, H. Ghiabi²

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.1, pp. 53-74, 2008, DOI:10.3970/cmes.2008.023.053

Abstract This paper deals with the problem of the consolidation of a composite consisting of alternate layers of soft clay and a granular material. A series of experiments were conducted on components to develop the constitutive models that can be implemented in a computational approach. The constitutive response of the soft clay is represented by a poro-elasto-plastic Cam clay-based model and the granular medium by an elasto-plastic model with a Drucker-Prager type failure criterion and a non-associated flow rule. The computational poro-elasto-plastic model is used to calibrate the experimental results derived from the one-dimensional tests and to establish the influence of… More >

L. Parussini¹, V. Pediroda²

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.1, pp. 29-52, 2008, DOI:10.3970/cmes.2008.023.029

Abstract In this paper different Polynomial Chaos methods coupled to Fictitious Domain approach have been applied to one- and two- dimensional elliptic problems with multi uncertain variables in order to compare the accuracy and convergence of the methodologies. Both intrusive and non-intrusive methods have been considered, with particular attention to their employment for quantification of geometric uncertainties. A Fictitious Domain approach with Least-Squares Spectral Element approximation has been employed for the analysis of differential problems with uncertain boundary domains. Its main advantage lies in the fact that only a Cartesian mesh, that represents the enclosure, needs to be generated. Excellent accuracy… More >