Open Access
ARTICLE
Xiaoming Zhang1, Xingxin Xu1,2, Yuqing Wang1
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.100.001
Abstract Orthogonal polynomial approach has been used to deal with the wave propagation in structures that have finite dimension in only one direction, such as horizontally infinite flat plates, axially infinite hollow cylinders. In order to solve wave propagation in two-dimensional piezoelectric rod with rectangular cross section, i.e. the piezoelectric plate with finite dimensions in two directions, an extended orthogonal polynomial approach is proposed in this paper. For validation and illustration purposes, the proposed approach is applied to solving the wave propagation in a square steel rod. The results obtained are in good agreement with the results from the semi-analytical finite… More >
Open Access
ARTICLE
F. Yang1, C.L. Fu2, X.X. Li1
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 19-29, 2014, DOI:10.3970/cmes.2014.100.019
Abstract Numerical differentiation is a classical ill-posed problem. The generalized Tikhonov regularization method is proposed to solve this problem. The error estimates are obtained for a priori and a posteriori parameter choice rules, respectively. Numerical examples are presented to illustrate the validity and effectiveness of this method. More >
Open Access
ARTICLE
S,erson L. Gonzaga de Oliveira1, Jéssica Renata Nogueira1, João Manuel R. S. Tavares2
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 31-57, 2014, DOI:10.3970/cmes.2014.100.031
Abstract Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay and/or Voronoi tessellations is presented. More >
Open Access
ARTICLE
T.A. Elgohary1, L. Dong2, J.L. Junkins3, S.N. Atluri4
CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 59-84, 2014, DOI:10.3970/cmes.2014.100.059
Abstract In this study, we consider ill-posed time-domain inverse problems for dynamical systems with various boundary conditions and unknown controllers. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables. Radial Basis Functions (RBFs) are assumed as trial functions for the mixed variables in the time domain. A simple collocation method is developed in the time-domain, with Legendre-Gauss-Lobatto nodes as RBF source points as well as collocation points. The duffing optimal control problem with various prescribed initial and final conditions, as well as the orbital… More >
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