A. Papacharalampopoulos², G. F. Karlis², A. Charalambopoulos³, D. Polyzos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 45-74, 2010, DOI:10.3970/cmes.2010.058.045

Abstract A Boundary Element Method (BEM) for solving two (2D) and three dimensional (3D) dynamic problems in materials with microstructural effects is presented. The analysis is performed in the frequency domain and in the context of Mindlin's Form II gradient elastic theory. The fundamental solution of the differential equation of motion is explicitly derived for both 2D and 3D problems. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative is exploited for the proposed BEM formulation. The global boundary of the analyzed domain is discretized into quadratic line… More >

Yunhua Li^1,2, Yunze Li³, Chieh-Li Chen⁴, Cha’o-Kuang Chen⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.1, pp. 1-14, 2010, DOI:10.3970/cmes.2010.058.001

Abstract Addressing the identification problem of the general Lagrange multiplier in the He's variational iteration method, this paper proposes a new kind of method based on Duhamel's principle for the dynamic system response analysis. In this method, we have constructed an analytical iteration formula in terms of the convolution for the residual error at the nth iteration, and have given a new interpretation to He's variational iteration method. The analysis illustrates that the computational result of this method is equal to that of He's variational iteration method on the assumption of considering the impulse response of the linear parts, or equal… More >

Sheng-Hu Ding^1,2, Xing Li², Yue-Ting Zhou^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 43-84, 2010, DOI:10.3970/cmes.2010.056.043

Abstract In this paper, the crack-tip fields in bonded functionally graded finite strips are studied. Different layers may have different nonhomogeneity properties in the structure. A bi-parameter exponential function was introduced to simulate the continuous variation of material properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. Various internal cracks and edge crack and crack crossing the interface configurations are investigated, respectively. The asymptotic stress field near the tip of a crack crossing the interface is examined and it is shown that, unlike the corresponding stress field… More >

Letícia Fleck Fadel Miguel¹, Ignacio Iturrioz², Jorge Daniel Riera³

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 1-16, 2010, DOI:10.3970/cmes.2010.056.001

Abstract Numerical predictions of the failure load of large structures, accounting for size effects, require the adoption of appropriate constitutive relations. These relations depend on the size of the elements and on the correlation lengths of the random fields that describe material properties. The authors proposed earlier expressions for the tensile stress-strain relation of concrete, whose parameters are related to standard properties of the material, such as Young's modulus or specific fracture energy and to size. Simulations conducted for a typical concrete showed that as size increases, the effective stress-strain diagram becomes increasingly linear, with a sudden rupture, while at the… More >

Ying Liu¹, Yufeng Nie², Weiwei Zhang², Lei Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 89-110, 2010, DOI:10.3970/cmes.2010.055.089

Abstract In the light of the ideas and treatment technologies about molecular dynamics simulation and bubble meshing, a new approach of node placement for the meshless method called node placement method by bubble simulation (NPBS method), is proposed. Nodes are seen as the centers of the bubbles which can be moved by their interacting forces. Through dynamic simulation, bubbles are placed into a near-optimal configuration, and the centers of bubbles will form a good-quality node distribution in the domain. This process doesn't need updating the mesh connection constantly, i.e., is totally meshfree. Some example results show that the uniform point sets… More >

Surkay D. Akbarov^1,2,3, Mugan S. Guliev⁴, Ramazan Tekercioglu⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 1-32, 2010, DOI:10.3970/cmes.2010.055.001

Abstract Dispersion relations of axisymmetric longitudinal wave propagation in a finite pre-strained compound (bi-material) cylinder made from high elastic incompressible materials are investigated within the scope of a piecewise homogeneous body model utilizing three-dimensional linearized theory wave propagation in the initially stressed body. The materials of the inner and outer cylinders are assumed to be neo-Hookean. The numerical results regarding the influence of the initial strains in the inner and outer cylinders on the wave dispersion are presented and discussed. These results are obtained for the case where the material of the inner solid cylinder is stiffer than that of the… 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 >

A. Colombo¹, U. Galvanetto²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.3, pp. 235-254, 2009, DOI:10.3970/cmes.2009.053.235

Abstract The paper addresses the problem of computing the stable manifolds of equilibria and limit cycles of saddle type in piecewise smooth dynamical systems. All singular points that are generically present along one-dimensional or two-dimensional manifolds are classified and such a classification is then used to define a method for the numerical computation of the stable manifolds. Finally the proposed method is applied to the case of a stick-slip oscillator. More >

Yi W. Wan¹, Huan J. Keh²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 73-94, 2009, DOI:10.3970/cmes.2009.053.073

Abstract The problem of the rotation of a rigid particle of revolution about its axis in a viscous fluid is studied theoretically in the steady limit of low Reynolds number. The fluid is allowed to slip at the surface of the particle. A singularity method based on the principle of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solution for the fluid velocity field that satisfies the boundary condition at infinity. The slip condition on the surface of… More >

Yu Miao¹, Qiao Wang¹, Bihai Liao^1,2, Junjie Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.053.001

Abstract As a truly meshless method, the Hybrid Boundary Node method (Hybrid BNM) does not require a `boundary element mesh', either for the purpose of interpolation of the solution variables or for the integration of `energy'. This paper presents a further development of the Hybrid BNM to the 2D elastodynamics. Based on the radial basis function (RBF) and the Hybrid BNM, it presents an inherently meshless, boundary-only technique, which named dual hybrid boundary node method (DHBNM), for solving 2D elastodynamics. In this study, the RBFs are employed to approximate the inhomogeneous terms via dual reciprocity method (DRM), while the general solution… More >