J. Lin¹, W. Chen^1,2, C. S. Chen³, X. R. Jiang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.6, pp. 485-505, 2013, DOI:10.3970/cmes.2013.094.485

Abstract To alleviate the difficulty of dense matrices resulting from the boundary knot method, the concept of the circulant matrix has been introduced to solve axi-symmetric Helmholtz problems. By placing the collocation points in a circular form on the surface of the boundary, the resulting matrix of the BKM has the block structure of a circulant matrix, which can be decomposed into a series of smaller matrices and solved efficiently. In particular, for the Helmholtz equation with high wave number, a large number of collocation points is required to achieve desired accuracy. In this paper, we present an efficient circulant boundary… More >

L.L. Chen¹, H.B. Chen², C.J. Zheng³

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.6, pp. 459-483, 2013, DOI:10.3970/cmes.2013.094.459

Abstract A coupling algorithm based on the finite element method and the wideband fast multipole boundary element method (FEM/wideband FMBEM) is proposed for the simulation of fluid-structure interaction and structural-acoustic sensitivity analysis using the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. The FEM/Wideband FMBEM algorithm makes it possible to predict the effects of arbitrarily shaped vibrating structures on the sound… More >

E. Viola¹, F. Tornabene¹, E. Ferretti¹, N. Fantuzzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.5, pp. 421-458, 2013, DOI:10.3970/cmes.2013.094.421

Abstract In this paper, an advanced version of the classic GDQ method, called the Generalized Differential Quadrature Finite Element Method (GDQFEM) is formulated to solve plate elastic problems with inclusions. The GDQFEM is compared with Cell Method (CM) and Finite Element Method (FEM). In particular, stress and strain results at fiber/matrix interface of dissimilar materials are provided. The GDQFEM is based on the classic Generalized Differential Quadrature (GDQ) technique that is applied upon each sub-domain, or element, into which the problem domain is divided. When the physical domain is not regular, the mapping technique is used to transform the fundamental system… More >

C. Delprete¹, F. Freschi², M. Repetto², C. Rosso¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.5, pp. 397-420, 2013, DOI:10.3970/cmes.2013.094.397

Abstract The growing necessity of accuracy in analyzing engineering problems requires more detailed and sophisticated models. Those models can include multiphysics interactions, that, sometimes, are highly nonlinear and the application of the superposition principle is then not possible. The cell method can be suitably used to study nonlinear multiphysics problems, because its theoretical framework for the physical laws is intrinsically multiphysics. In this way it is possible to take into account the mutual effects between different physics. Within the cell method framework, the coupling terms can be directly formulated in terms of the global variables used for the solution of the… More >

F. Freschi¹, L. Giaccone¹, M. Repetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.5, pp. 371-395, 2013, DOI:10.3970/cmes.2013.094.371

Abstract The study of induction heating systems from the electromagnetic point of view is still a challenging task for several reasons: the problem under analysis is strictly multiphysics because it involves the coupled electromagnetic and thermal phenomena; both coupled physics have nonlinear behavior; nonlinearities are of different kinds, both depending on the single phenomenon and on the coupling terms. The aim of the paper is to show that the cell method, based on the use of Tonti diagrams, can handle efficiently this kind of problems. The proposed magneto-thermal numerical procedure is firstly described in its theoretical aspects and then it is… More >

E. Viola¹, F. Tornabene¹, E. Ferretti¹, N. Fantuzzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.4, pp. 331-369, 2013, DOI:10.3970/cmes.2013.094.331

Abstract In the present paper the Generalized Differential Quadrature Finite Element Method (GDQFEM) is applied to deal with the static analysis of plane state structures with generic through the thickness material discontinuities and holes of various shapes. The GDQFEM numerical technique is an extension of the Generalized Differential Quadrature (GDQ) method and is based on the idea of conventional integral quadrature. In particular, the GDQFEM results in terms of stresses and displacements for classical and advanced plane stress problems with discontinuities are compared to the ones by the Cell Method (CM) and Finite Element Method (FEM). The multi-domain technique is implemented… More >

E. Viola¹, F. Tornabene¹, E. Ferretti¹, N. Fantuzzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.4, pp. 301-329, 2013, DOI:10.3970/cmes.2013.094.301

Abstract The aim of this work is to study the static behavior of 2D soft core plane state structures. Deflections and inter-laminar stresses caused by forces can have serious consequences for strength and safety of these structures. Therefore, an accurate identification of the variables in hand is of considerable importance for their technical design. It is well-known that for complex plane structures there is no analytical solution, only numerical procedures can be used to solve them. In this study two numerical techniques will be taken mainly into account: the Generalized Differential Quadrature Finite Element Method (GDQFEM) and the Cell Method (CM).… More >

Martino Pani¹, Fulvia Taddei¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.4, pp. 279-300, 2013, DOI:10.3970/cmes.2013.094.279

Abstract The Cell Method (CM) is a numerical method to solve field equations starting from its direct algebraic formulation. For two-dimensional problems it has been demonstrated that using simplicial elements with an affine interpolation, the CM obtains the same fundamental equation of the Finite Element Method (FEM); using the quadratic interpolation functions, the fundamental equation differs depending on how the dual cell is defined. In spite of that, the CM can still provide the same convergence rate obtainable with the FEM. Particularly, adopting a uniform triangulation and basing the dual cells on the Gauss points of the primal edges, the CM… More >

J.L. Morales¹, I. Alhama¹, M. Alcaraz¹, F. Alhama

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.3, pp. 261-277, 2013, DOI:10.32604/cmes.2013.094.261

Abstract In this paper, the propagation of 2-D, transversal elastic waves is simulated by using the network method. The spatially discretized wave equation is the basis for designing the model of the volume element which contains as many components as addends in the governing equation. The whole network model, including the boundary conditions, is run in a suitable circuit simulation code such as PSpice with a relatively small computational time. The rules for the design are very few since there is a special component in the libraries of such codes, named controlled source, that is capable of implementing any kind of… More >

Bingfei Liu¹, Guansuo Dui^2,3, Lijun Xue², Benming Xie¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.3, pp. 239-260, 2013, DOI:10.32604/cmes.2013.094.239

Abstract Analytical solutions are derived for the macroscopic behaviors of a Shape Memory Alloy (SMA) thick-walled cylinder subjected to internal pressure and radial temperature gradient. The Tresca transformation criterion and linear hardening are used. Equations are given for the radial and circumferential stresses, transformation strains and martensite volume fractions at both the elastic step and the transformation step. Numerical results are presented and in good agreement with the finite element simulations. More >