Roman Chapko¹, B. Tomas Johansson²

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 105-128, 2012, DOI:10.3970/cmes.2012.085.105

Abstract We consider a Cauchy problem for the Laplace equation in a 3-dimen -sional semi-infinite domain that contains a bounded inclusion. The canonical situation is the upper half-space in I\tmspace -.1667em R3 containing a bounded smooth domain. The function value of the solution is specified throughout the plane bounding the upper half-space, and the normal derivative is given only on a finite portion of this plane. The aim is to reconstruct the solution on the surface of the bounded inclusion. This is a generalisation of the situation in Chapko and Johansson (2008) to three-dimensions and with Cauchy data only partially given.… More >

V.G. Yakhno¹, H.Çerdik Yaslan²

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 295-310, 2011, DOI:10.3970/cmes.2011.081.295

Abstract The time-dependent differential equations of elasticity for 3D quasicrystals are considered in the paper. These equations are written in the form of a vector partial differential equation of the second order with symmetric matrix coefficients. The Green's function is defined for this vector partial differential equation. A new method of the numerical computation of values of the Green's function is proposed. This method is based on the Fourier transformation and some matrix computations. Computational experiments confirm the robustness of our method for the computation of the time-dependent Green's function in icosahedral quasicrystals. More >

Y.C. Shiah¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095

Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to… More >

A. Sellier, N. Ghalia

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.1, pp. 25-50, 2011, DOI:10.3970/cmes.2011.078.025

Abstract The Green tensor complying with anisotropic slip conditions at the surface of a plane, impermeable, motionless and slipping wall is theoretically obtained and an efficient numerical method is proposed to accurately compute at a very reasonable cpu time cost each of its Cartesian component. The accuracy of the advocated numerical strategy is tested against the Maple Software and the employed procedure makes it possible to calculate the Green tensor for a non-isotropic slip condition at a cpu time cost comparable with the one needed for the less complicated isotropic Navier condition. More >

L. Hedhili, A. Sellier, L. Elasmi, F. Feuillebois

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 137-170, 2011, DOI:10.3970/cmes.2011.073.137

Abstract The motion of a solid particle embedded in a viscous fluid in a closed container requires a precise account of wall effects when in creeping flow. The boundary integral method, which amounts to solving a Fredholm integral equation for the stress on the particle and walls, is used here. The accuracy of the method is improved by using curvilinear six-node triangular boundary elements, the size of which is specially adapted to the particle shape and position with respect to walls. The method is applied to resolve the case of a moving particle in a parallelepiped container. It is validated by… More >

Roman Chapko¹, B. Tomas Johansson², Oleh Sobeyko¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 57-76, 2010, DOI:10.3970/cmes.2010.062.057

Abstract We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical… More >

Y.C. Chen¹, Chyanbin Hwu²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 31-50, 2010, DOI:10.3970/cmes.2010.057.031

Abstract The Green's function for anisotropic bimaterials has been investigated around three decades ago. Since the mathematical formulation of piezoelectric elasticity can be organized into the same form as that of anisotropic elasticity by just expanding the dimension of the corresponding matrix to include the piezoelectric effects, the extension of the Green's function to piezoelectric bimaterials can be obtained immediately through the associated anisotropic bimaterials. In this paper, the Green's function for the bimaterials bonded together with one anisotropic material and one piezoelectric material is derived by applying Stroh's complex variable formalism with the aid of analytical continuation method. For this… More >

D. Soares Jr.¹, J. Sladek², V. Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 115-140, 2009, DOI:10.3970/cmes.2009.050.115

Abstract In recent years the idea of using mesh-free or mesh-less methods for numerical solution of partial differential equations has received much attention, due to their potential advantage in eliminating the costly effort of mesh generation and re-meshing. A variety of meshless methods has been proposed so far. Many of them are derived from a weak-form formulation on global domain or a set of local subdomains. In the global formulation background cells are required for the integration of the weak form. In methods based on local weak-form formulation no cells are required and therefore they are often referred to as truly… More >

J.C.Campbell¹, R.Vignjevic¹, M.Patel¹, S.Milisavljevic¹

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.049.001

Abstract This paper presents research towards the development of an analysis technique for predicting the interaction of large ocean waves with ships and offshore structures specifically with respect to the extent of deck submersion, impact loads and the level of structural damage caused. The coupled SPH - Finite Element approach is used, where the water is modeled with SPH and the structure with shell or continuum finite elements. Details of the approach are presented, including the SPH-FE contact and the fluid boundary conditions. Simulation results show that the method can correctly represent the behavior of a floating structure and the structural… 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 >