J. Sladek¹, V. Sladek¹, M. Wünsche², Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 223-252, 2009, DOI:10.3970/cmes.2009.054.223

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve the interface crack problem between two dissimilar anisotropic elastic solids. Both stationary and transient mechanical and thermal loads are considered for two-dimensional (2-D) problems in this paper. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variations of the displacements and temperature are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, one obtains… More >

Delfim Soares Jr.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 201-222, 2009, DOI:10.3970/cmes.2009.054.201

Abstract In this work, meshless methods based on the local Petrov-Galerkin approach are employed for the time-domain analysis of interacting fluid and solid systems. For the spatial discretization of the acoustic fluid and elastodynamic solid sub-domains involved in the coupled analyses, MLPG formulations adopting Gaussian weight functions as test functions are considered, as well as the moving least square method is used to approximate the incognita fields. For time discretization, the Houbolt's method is adopted. The fluid-solid coupled analysis is accomplished by an iterative algorithm. In this iterative approach, each sub-domain of the global model is analysed independently (as an uncoupled… More >

Hua Li¹, Shantanu S. Mulay¹, Simon See²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 147-200, 2009, DOI:10.3970/cmes.2009.054.147

Abstract In this paper, the stability characteristics of a novel strong-form meshless method, called the random differential quadrature (RDQ), are studied using the location of zeros or roots of its characteristic polynomials with respect to unit circle in complex plane by discretizing the domain with the uniform or random field nodes. This is achieved by carrying out the RDQ method stability analysis for the 1st-order wave, transient heat conduction and transverse beam deflection equations using both the analytical and numerical approaches. The RDQ method extends the applicability of the differential quadrature (DQ) method over irregular domain, discretized by randomly or uniformly… More >

D. C. Knupp¹, A. J. Silva Neto², W. F. Sacco³

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.2, pp. 121-146, 2009, DOI:10.3970/cmes.2009.054.121

Abstract The inverse analysis of radiative transfer in participating media has several practical applications. In most cases, the inverse problem is formulated implicitly and the solution is given by the minimization of an objective function. Gradient based methods have largely been used for that purpose, but it has been observed in recent years an increasing interest in the use of stochastic methods. In this work, it is proposed the use of the Luus-Jaakola method and the Particle Collision Algorithm. The former is a random search optimization method that has been successfully employed mainly in chemical engineering, and the latter is a… More >

Chien-Ching Ma^1,2, Jui-Mu Lee²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 87-120, 2009, DOI:10.3970/cmes.2009.054.087

Abstract In this study, the two-dimensional problem of elastic, electric, and magnetic fields induced by generalized line forces and screw dislocations applied in a functionally graded magnetoelectroelastic layered half-plane is analyzed. It is assumed that the material properties vary exponentially along the thickness direction. The full-field solutions for the transversely isotropic magnetoelectroelastic nonhomogeneous layered half-plane are obtained using the Fourier-transform technique. For the case that material properties are continuous at the interface, it is shown that all magnetoelectroelastic fields are continuous at the interface. Furthermore, this functionally graded layered half-plane has the identical contour slopes for the generalized stress \pmbsy(j)across the… More >

Wen Chen^1,2, Zhuojia Fu¹, Xing Wei¹

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 65-86, 2009, DOI:10.3970/cmes.2009.054.065

Abstract This study investigates the singular boundary method (SBM), a novel boundary-type meshless method, in the numerical solution of potential problems. Our finding is that the SBM can not obtain the correct solution in some tested cases, in particular, in the cases whose solution includes a constant term. To remedy this drawback, this paper presents an improved SBM formulation which is a linear sum of the fundamental solution adding in a constant term. It is stressed that this SBM approximation with the additional constant term has to satisfy the so-called moment condition in order to guarantees the uniqueness of the solution.… More >

R. Avila¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 15-64, 2009, DOI:10.3970/cmes.2009.054.015

Abstract The Meshless Local Petrov Galerkin (MLPG) method is used to solve the non-steady two dimensional Navier-Stokes equations. Transient laminar flow field calculations have been carried out in domains wherein certain surfaces have: (i) a sliding motion, (ii) a harmonic motion, (iii) an undulatory movement, and (iv) a contraction-expansion movement. The weak form of the governing equations has been formulated in a Cartesian coordinate system and taking into account the primitive variables of the flow field. A fully implicit pressure correction approach, which requires at each time step an iterative process to solve in a sequential manner the equations which govern… More >

M. Irízar, L. D. Câmara, A. J. Silva Neto, O. Llanes

CMES-Computer Modeling in Engineering & Sciences, Vol.54, No.1, pp. 1-14, 2009, DOI:10.3970/cmes.2009.054.001

Abstract Modeling of Chromatography allows a better understanding and development of new techniques to be applied at industrial level, although it's relatively complex. The models of this process are represented by systems of partial differential equations with non linear parameters difficult to estimate generally, which constitutes an inverse problem. In general there aren't analytical solutions and therefore numerical methods should be used for their direct solutions. Frequently typical boundary conditions are considered, but it's convenient to study different approaches for those. Evolutionary Computation has been used successfully in many problems of diverse areas for searching in complex spaces. Considering previous works… More >

A. Carpinteri¹, M. Paggi^1,2, G. Zavarise³

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.3, pp. 303-326, 2009, DOI:10.3970/cmes.2009.053.303

Abstract The stick-slip instability is a typical manifestation of the nonlinearity of the frictional response of rough surfaces. As recently demonstrated by several researchers, the problem of contact loss is also inherently connected to the stick-slip instability and it has been detected both in elastically soft materials, such as rubber or gelatine, and in elastic stiff materials, such as for earthquake faults. Treating the problem of tangential contact in the framework of micromechanical contact models, the effect of the phenomenon of contact loss on the micro-slip behavior of rough surfaces is herein investigated. To this aim, the stick and slip components… More >

D. Gawin¹, L. Sanavia²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.3, pp. 255-302, 2009, DOI:10.3970/cmes.2009.053.255

Abstract This paper presents a unified mathematical approach to model the hydro-thermo-mechanical behavior of saturated and partially saturated porous media by considering the effects of air dissolved in liquid water. The model equations are discretized by means of the Finite Element method. A correspondingly updated code is used to analyze two examples; the first one is the well known Liakopoulos test, i.e. the drainage of liquid water from a 1m column of sand, which is used to validate numerically the model here developed. As second example, a biaxial compression test of undrained dense sands where cavitation takes place at strain localization… More >