S. Hagihara¹, M. Tsunori², T. Ikeda³, N. Miyazaki³

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 63-72, 2007, DOI:10.3970/cmes.2007.017.063

Abstract The element-free Galerkin (EFG) method is applied to the calculation of elastic-plastic fracture mechanics parameters such as the J-integral and T*-integral. The fields of displacement, strain and stress for a crack problem are obtained using the elastic-plastic EFG method. Then the elastic-plastic fracture mechanics parameters J-integral and T*-integral are calculated from path and domain integrals. In the finite element analysis, paths for the path integral and domains for the domain integral are selected depending on finite element mesh division. On the other hand, they can be arbitrarily selected in the EFG method, and we can… More >

K. Hashiguchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 55-62, 2007, DOI:10.3970/cmes.2007.017.055

Abstract Constitutive equation describing the mechanical properties of material has to be formulated in an identical form independent of coordinate systems by which it is described even if there exist any mutual configuration and/or mutual rotation between the material and coordinate systems. This mechanical requirement is attained by describing rate variables as corotational rate tensors with objectivity in constitutive equations in rate form. Besides, in order to use the material-time derivative of yield condition as a consistency condition it has to be replaced to the corotational derivative. In this note a general corotational rate for tensors More >

Ivan Christov¹, C.I. Christov², P.M. Jordan³

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 47-54, 2007, DOI:10.3970/cmes.2007.017.047

Abstract Two widely-used weakly-nonlinear models of acoustic wave propagation --- the inviscid Kuznetsov equation (IKE) and the Lighthill--Westervelt equation (LWE) --- are investigated numerically using a Godunov-type finite-difference scheme. A reformulation of the models as conservation laws is proposed, making it possible to use the numerical tools developed for the Euler equations to study the IKE and LWE, even after the time of shock-formation. It is shown that while the IKE is, without qualification, in very good agreement with the Euler equations, even near the time of shock formation, the same cannot generally be said for More >

G. Dziatkiewicz¹ and P. Fedelinski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 35-46, 2007, DOI:10.3970/cmes.2007.017.035

Abstract The aim of the present work is to show the formulation and application of the dual reciprocity boundary element method (BEM) to free vibrations of two-dimensional piezoelectric structures. The piezoelectric materials are modelled as homogenous, linear -- elastic, transversal isotropic and dielectric. Displacements and electric potentials are treated as generalized displacements and tractions and electric charge flux densities are treated as generalized tractions. The static fundamental solutions, which are required in the proposed approach, are derived using the Stroh formalism. The domain inertial integral is transformed to the equivalent boundary integral using the dual reciprocity More >

D. Soares Jr.^1,2, W.J. Mansur¹, D.L. Lima³

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 19-34, 2007, DOI:10.3970/cmes.2007.017.019

Abstract The present paper discussion is concerned with the development of robust and efficient algorithms to model propagation of interacting acoustic and elastic waves. The paper considers acoustic-elastic, acoustic-acoustic and elastic-elastic partitioned analyses of coupled systems; however, the focus here is the acoustic-elastic coupling considering finite elements and the acoustic-acoustic coupling considering finite elements and finite differences (other coupling procedures can be implemented analogously). One important feature of the algorithms presented is that they allow considering different time-steps for different sub-domains; so it is possible to substantially improve efficiency, accuracy and stability of the central difference More >

Chein-Shan Liu¹, Li-Wei Liu², Hong-Ki Hong²

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 1-18, 2007, DOI:10.3970/cmes.2007.017.001

Abstract In this paper we are concerned with the parameters identification of the inverse heat conduction problems governed by linear parabolic partial differential equations (PDEs). It is the first time that one can construct a closed-form estimation method for the inverse thermal problems of estimating the spatial-dependent thermophysical parameters. The key points hinge on an establishment of a one-step group preserving scheme (GPS) for the semi-discretization of PDEs, as well as a closed-form solution of the resulting algebraic equations. The new method, namely the Lie-group estimation method, has four advantages: it does not require any prior More >

Mira Mitra¹, S. Gopalakrishnan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.1, pp. 49-68, 2006, DOI:10.3970/cmes.2006.015.049

Abstract In this paper, a 2-D Wavelet based Spectral Finite Element (WSFE) is developed and is used to study wave propagation in an isotropic plate. Here, first, wavelet approximation is done in both temporal and one spatial (lateral) dimension to reduce the governing partial differential wave equations to a set of Ordinary Differential Equations (ODEs). Daubechies compactly supported orthogonal scaling functions are used as basis which allows finite domain analysis and easy imposition of initial/boundary conditions. However, the assignment of initial and boundary conditions in time and space respectively, are done following two different methods. Next,… More >

A. Frangi¹, L. Ghezzi, P. Faure-Ragani²

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.1, pp. 41-48, 2006, DOI:10.3970/cmes.2006.015.041

Abstract Three dimensional magneto-mechanical problems at low frequency are addressed by means of a coupled fast Boundary Element - Finite Element approach with total scalar potential and focusing especially on the issue of global force calculation on movable ferromagnetic parts. The differentiation of co-energy in this framework and the use of Maxwell tensor are critically discussed and the intrinsic links are put in evidence. Three examples of academic and industrial applications are employed for validation. More >

P. Fedelinski¹, R. Gorski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.1, pp. 31-40, 2006, DOI:10.3970/cmes.2006.015.031

Abstract The aim of the present work is to analyze and optimize plates in plane strain or stress with stiffeners subjected to dynamic loads. The reinforced structures are analyzed using the coupled boundary and finite element method. The plates are modeled using the dual reciprocity boundary element method (DR-BEM) and the stiffeners using the finite element method (FEM). The matrix equations of motion are formulated for the plate and stiffeners. The equations are coupled using conditions of compatibility of displacements and equilibrium of tractions along the interfaces between the plate and stiffeners. The final set of… More >

A. Milazzo¹, I. Benedetti², C. Orlando³

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.1, pp. 17-30, 2006, DOI:10.3970/cmes.2006.015.017

Abstract A boundary integral formulation and its numerical implementation are presented for the analysis of magneto electro elastic media. The problem is formulated by using a suitable set of generalized variables, namely the generalized displacements, which are comprised of mechanical displacements and electric and magnetic scalar potentials, and generalized tractions, that is mechanical tractions, electric displacement and magnetic induction. The governing boundary integral equation is obtained by generalizing the reciprocity theorem to the magneto electro elasticity. The fundamental solutions are calculated through a modified Lekhnitskii's approach, reformulated in terms of generalized magneto-electro-elastic displacements. To assess the More >