H.X. Wang, S.X. Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 253-274, 2008, DOI:10.3970/cmes.2008.035.253

Abstract In the meshfree cohesive crack method, the discrete crack is modeled by a set of cohesive crack segments which can be arbitrarily oriented. Propagation of the crack is achieved by activation of crack surfaces at individual nodes, so no representation of the crack surface is needed. The crack is modeled by a local enrichment of the test and trial functions with sign function, so that discontinuities are along the direction of the crack. A set of cracking rules is developed to avoid spurious cracking. More >

De-hao Yu¹ ,Hong-ying Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 227-252, 2008, DOI:10.3970/cmes.2008.035.227

Abstract In this paper, we apply the artificial boundary method to solve a three-dimensional nonlinear interface problem on an unbounded domain. A spherical or ellipsoidal surface as the artificial boundary is introduced. The exact artificial boundary conditions are derived explicitly in terms of an infinite series and then the well-posedness of the coupled weak formulation in a bounded domain, which is equivalent to the original problem in the unbounded domain, is obtained. The error estimate depends on the mesh size, the term after truncating the infinite series and the location of the artificial boundary. Some numerical More >

Chein-Shan Liu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 157-180, 2008, DOI:10.3970/cmes.2008.035.157

Abstract For an inverse vibration problem of nonlinear mechanical system to estimate displacement- and velocity-dependent restoring force, we transform the equation of motion into a parabolic type partial differential equation (PDE). Then by a semi-discretization of the PDE, the inverse vibration problem is formulated as a multi-dimensional two-point boundary value problem with unknown sources, allowing a closed-form estimation through a Lie-group shooting method to construct the restoring force surface over phase plane. Only one set of displacements measured at sampling time points is used in the estimation. The new method does not require to assume a More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 91-112, 2008, DOI:10.3970/cmes.2008.035.091

Abstract We consider the inverse Cauchy problems for Laplace equation in simply and doubly connected plane domains by recoverning the unknown boundary value on an inaccessible part of a noncircular contour from overspecified data. A modified Trefftz method is used directly to solve those problems with a simple collocation technique to determine unknown coefficients, which is named a modified collocation Trefftz method (MCTM). Because the condition number is small for the MCTM, we can apply it to numerically solve the inverse Cauchy problems without needing of an extra regularization, as that used in the solutions of More >

S.-W. Na¹, L.F. Kallivokas²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 73-90, 2008, DOI:10.3970/cmes.2008.035.073

Abstract We discuss simple numerical schemes, termed continuation schemes, for detecting the location and shape of a scatterer embedded in a host acoustic medium, when considering scant measurements of the scattered acoustic pressure in the vicinity (near- or far-field) of the obstacle. The detection is based on incomplete information, i.e., the measurement stations are distributed in the backscatter region and do not circumscribe the sought scatterer. We consider sound-hard scatterers, and use boundary integral equations for the underlying numerical scheme. We favor amplitude-based misfit functionals, and use frequency- and directionality-continuation schemes to resolve the scatterer's location More >

C. Jeong¹, L.F. Kallivokas²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 49-72, 2008, DOI:10.3970/cmes.2008.035.049

Abstract We discuss the inverse scattering problem of identifying the shape and location of a rigid scatterer fully buried in a homogeneous halfplane, when illuminated by surficial (line) wave sources generating SH waves. To this end, we consider the full-waveform response of the coupled host-obstacle system in the frequency domain, and employ the apparatus of partial-differential-equation-constrained optimization, augmented with total differentiation for tracking shape evolutions across inversion iterations, and specialized continuation schemes in lieu of formal regularization. We report numerical results that provide evidence of algorithmic robustness for detecting a variety of shapes, including elliptically- and More >

Zheng Juan^1,2,3, Long Shuyao^1,2, Xiong Yuanbo^1,2, Li Guangyao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 137-154, 2008, DOI:10.3970/cmes.2008.034.137

Abstract In this paper, the meshless radial point interpolation method (RPIM) is applied to carry out a topology optimization design for the continuum structure. Considering the relative density of nodes as a design variable, and the minimization of compliance as an objective function, the mathematical formulation of the topology optimization design is developed using the SIMP (solid isotropic microstructures with penalization) interpolation scheme. The topology optimization problem is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design for the continuum structure, and can More >

A.N. Guz¹, J.J.Rushchitsky¹, I.A.Guz²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 139-156, 2008, DOI:10.3970/cmes.2008.026.139

Abstract The basic approach is offered for problems of nanocomposites and their mechanical properties, which includes a short review of modern problems in nanomechanics of materials. The fibrous carbon-polymer composites with carbon or graphite microfibers or carbon nanotubes are especially discussed. The basic model of the linear or nonlinear elastically deforming micro- and nanocomposites is considered. Within the framework of this model, the comparative computer modeling is performed. The modeling permits to observe the features in prediction of values of basic mechanical constants. These results are utilized on next step of modeling -- studying the peculiarities More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Shekarchi², Mohammad Rahimian²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 263-284, 2008, DOI:10.3970/cmes.2008.038.263

Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the More >

T. Jarak¹, J. Sorić¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 231-262, 2008, DOI:10.3970/cmes.2008.038.231

Abstract A new mixed meshless formulation based on the interpolation of both strains and displacements has been proposed for the analysis of plate deformation responses. Kinematics of a three dimensional solid is adopted and discretization is performed by the nodes located on the upper and lower plate surfaces. The governing equations are derived by employing the local Petrov-Galerkin approach. The approximation of all unknown field variables is carried out by using the same Moving Least Squares functions in the in-plane directions, while linear polynomials are applied in the transversal direction. The shear locking effect is efficiently More >