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 >

Xuefei He¹, Kian-Meng Lim^1,2,3, Siak-Piang Lim^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 21-48, 2008, DOI:10.3970/cmes.2008.035.021

Abstract The boundary element method (BEM) is known to have the advantage of reducing the dimension of problem by discretizing only the boundary of the domain. But it becomes less attractive for solving Poisson-type equations, due to the need to evaluate the domain integral which is computationally expensive. In this paper, we present the extension of a recently developed fast algorithm for Laplace equation, based on fast Fourier transform on multipoles (FFTM), to solve large scale 3D Poisson-type equations. We combined the Laplace solver with two fast methods for handling the domain integral based on fast More >

N. Shishido, T. Ikeda, N. Miyazaki

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 1-20, 2008, DOI:10.3970/cmes.2008.035.001

Abstract We propose an image correction method that will accurately measure full-field displacement in a microstructure using the digital image correlation method (DICM); the proposed method is suitable for use with laser-scanned images. Laser scanning microscopes have higher spatial resolution and deeper depth of field than optical microscopes, but errors in laser scanning position (time-dependent distortion) affect the accuracy of the DICM. The proposed image correction method involves the removal of both time-dependant and time-independent distortions. Experimental results using images of prescribed rigid-body motions demonstrate that the proposed correction method is capable of identifying and removing… More >

J. Sladek¹, V. Sladek², P. Solek¹, S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 273-300, 2008, DOI:10.3970/cmes.2008.034.273

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplace-transform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain, and each More >

K. Lee¹ and S.W. Lee ²

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 253-272, 2008, DOI:10.3970/cmes.2008.034.253

Abstract A geometrically nonlinear assumed strain formulation is used to develop a nine-node solid shell element with quadratic displacement through the thickness. The transversely quadratic element allows direct use of the constitutive equations developed for three-dimensional solids, which is convenient when material nonlinearity is involved. The nodal degrees of freedom associated with the quadratic terms in the assumed displacement through the thickness are statically condensed out at the element level. The results of numerical tests conducted on selected example problems demonstrate the validity and effectiveness of the present approach. For the cases involving linear elastic material, More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 227-252, 2008, DOI:10.3970/cmes.2008.034.227

Abstract A new numerical technique for solving generalized Sturm--Liouville problem d²w/dx² + q(x, λ )w = 0, b_l[ λ ,w(a)] = b_r[ λ ,w(b)] = 0 is presented. In is presented. In particular, we consider the problems when the coefficient q(x, λ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues. The same technique can be applied to a very wide class of More >

Y. C. Shiah¹, C. L. Tan², V.G. Lee³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 205-226, 2008, DOI:10.3970/cmes.2008.034.205

Abstract The main impediment to the development of efficient algorithms for the stress analysis of 3D generally anisotropic elastic solids using the boundary element method (BEM) and the local boundary integral equation (LBIE) meshless method over the years is the complexity of the fundamental solutions and the computational burden to evaluate them. The ability to analytically simplify and reduce them into as explicit a form as possible so that they can be directly computed will offer significant cost savings. In addition, they facilitate easy implementation using existing numerical algorithms with the above-mentioned methods that have been More >

Y.C. Cai¹ and H.H. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 179-204, 2008, DOI:10.3970/cmes.2008.034.179

Abstract The popular Shepard PU approximations are easy to construct and have many advantages, but they have several limitations, such as the difficulties in handling essential boundary conditions and the known problem of linear dependence regarding PU-based methods, and they are not the good choice for MLPG method. With the objective of alleviating the drawbacks of Shepared PU approximations, a new meshless PU-based Shepard and Least Square (SLS) interpolation is employed here to develop a new type of MLPG method, which is named as Local Meshless Shepard and Least Square (LMSLS) method. The SLS interpolation possesses… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 155-178, 2008, DOI:10.3970/cmes.2008.034.155

Abstract In this paper we propose a novel method for solving a nonlinear optimization problem (NOP) under multiple equality and inequality constraints. The Kuhn-Tucker optimality conditions are used to transform the NOP into a mixed complementarity problem (MCP). With the aid of (nonlinear complementarity problem) NCP-functions a set of nonlinear algebraic equations is obtained. Then we develop a fictitious time integration method to solve these nonlinear equations. Several numerical examples of optimization problems, the inverse Cauchy problems and plasticity equations are used to demonstrate that the FTIM is highly efficient to calculate the NOPs and MCPs. More >