Mingxu Yi¹, Yiming Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 229-244, 2012, DOI:10.3970/cmes.2012.088.229

Abstract In this paper, Haar wavelet operational matrix method is proposed to solve a class of fractional partial differential equations. We derive the Haar wavelet operational matrix of fractional order integration. Meanwhile, the Haar wavelet operational matrix of fractional order differentiation is obtained. The operational matrix of fractional order differentiation is utilized to reduce the initial equation to a Sylvester equation. Some numerical examples are included to demonstrate the validity and applicability of the approach. More >

Jiawei Xiang^1,2, Yanxue Wang³, Zhansi Jiang³, Jiangqi, Long¹, Guang Ma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 1-16, 2012, DOI:10.3970/cmes.2012.088.001

Abstract Two-dimensional wavelet-based numerical approximation using Hermite cubic spline wavelet on the interval (HCSWI) is proposed to solve stress intensity factors (SIFs) of plate structures. The good localization property of wavelets is used to approximate displacement fields by multi-scale bases of HCSWI. Example computations are performed for plates with a central crack and double edge cracks. The numerical results prove that, compared with the conventional finite element method and the analytical solutions, the new procedure are efficient in both its accuracy and its reduction of degree of freedoms (DOFs). More >

Zhibo Yang¹, Xuefeng Chen², Bing Li¹, Zhengjia He¹, Huihui Miao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 129-156, 2012, DOI:10.3970/cmes.2012.085.129

Abstract The implementation of the B-spline Wavelet on the Interval (BSWI) for curved shell elements with rectangular planform is presented in this paper. By aid of the general shell theory, cylinder shells, doubly-curved shallow shells and hyperbolic paraboloidal shells BSWI elements are formulated. Instead of traditional polynomial interpolation, scaling functions at certain scale have been adopted to form the shape functions and construct wavelet-based elements. Because of the good character of BSWI scaling functions, the BSWI curved shell elements combine the accuracy of wavelet-based elements approximation and the character of B-spline functions for structural analysis. Different from the flat shell elements,… More >

Bing Li^1,2, Hongbo Dong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 205-228, 2012, DOI:10.3970/cmes.2012.084.205

Abstract Different from single crack identification method, the number of cracks should be firstly identified, and then the location and depth of each crack can be predicted for multiple cracks identification technology. This paper presents a multiple crack identification algorithm for rotor using wavelet finite element method. Firstly, the changes in natural frequency of a structure with various crack locations and depths are accurately obtained by means of wavelet finite element method; and then the damage coefficient method is used to determine the number and region of cracks. Finally, by finding the points of intersection of three frequency contour lines in… More >

Jiawei Xiang¹, Toshiro Matsumoto², Yanxue Wang³, Zhansi Jiang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.3&4, pp. 269-294, 2011, DOI:10.3970/cmes.2011.081.269

Abstract Damages occurred in a structure will lead to changes in modal parameters (natural frequencies and modal shapes). The relationship between modal parameters and damage parameters (locations and depths) is very complicated. Single detection method using natural frequencies or modal shapes can not obtain robust damage detection results from the inevitably noise-contaminated modal parameters. To eliminate the complexity, a hybrid approach using both of wavelets on the interval (interval wavelets) method and wavelet finite element model-based method is proposed to detect damage locations and depths. To avoid the boundary distortion phenomenon, Interval wavelets are employed to analyze the finite-length modal shape… More >

Zhou YH^1,2, Wang XM², Wang JZ^1,2 , Liu XJ²

CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.2, pp. 137-160, 2011, DOI:10.3970/cmes.2011.077.137

Abstract In this paper, we present an efficient wavelet-based algorithm for solving a class of fractional vibration, diffusion and wave equations with strong nonlinearities. For this purpose, we first suggest a wavelet approximation for a function defined on a bounded interval, in which expansion coefficients are just the function samplings at each nodal point. As the fractional differential equations containing strong nonlinear terms and singular integral kernels, we then use Laplace transform to convert them into the second type Voltera integral equations with non-singular kernels. Certain property of the integral kernel and the ability of explicit wavelet approximation to the nonlinear… More >

Jiawei Xiang^1,2, Ming Liang^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 267-298, 2011, DOI:10.3970/cmes.2011.073.267

Abstract The importance of damage detection in structures has been widely recognized in mechanical and civil engineering. A new method is proposed to detect multiple damages based on frequency measurement. According to linear fracture mechanics theory, the damages are modeled by rotational springs. The first problem of interest is concerned with the construction of multi-scaling wavelet finite element model using Hermite cubic spline wavelet on the interval (HCSWI) in the forward problem analysis to obtain damages detection database. The second problem is the inverse problem analysis to determine the number of damages, their locations and depths based on the minimum Root-mean-square… More >

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

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 161-190, 2009, DOI:10.3970/cmes.2009.050.161

Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs over irregularly shaped domains. For a problem defined over Ω∈ℜ^d, the boundary of an irregularly shaped domain, Γ, is defined as a boundary curve that is a product of a Heaviside function along the normal direction and a piecewise continuous tangential curve. The link between the original wavelet based adaptive method presented in Libre, Emdadi, Kansa, Shekarchi, and Rahimian (2008, 2009) or LEKSR method and the generalized one is given through the use of simple Heaviside masking procedure. In addition… 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 proposed adaptive scheme can detect… More >

Zhi-Zhong Yan^1,2, Yue-Sheng Wang^1,3, Chuanzeng Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 59-88, 2008, DOI:10.3970/cmes.2008.038.059

Abstract In this paper, a numerical method based on the wavelet theory is developed for calculating band structures of 2D phononic crystals consisting of general anisotropic materials. After systematical consideration of the appropriate choice of wavelets, two types of wavelets, the Haar wavelet and Biorthogonal wavelet, are selected. Combined with the supercell technique, the developed method can be then applied to compute the band structures of phononic crystals with point or line defects. We illustrate the advantages of the method both mathematically and numerically. Particularly some representative numerical examples are presented for various material combinations (solid-solid, solid-fluid and fluid-fluid) with complex… More >