The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Xuefeng Chen - One of the best experts on this subject based on the ideXlab platform.

  • static and dynamic analysis of cylindrical shell by different kinds of b Spline Wavelet finite elements on the interval
    Engineering With Computers, 2020
    Co-Authors: Xingwu Zhang, Ruqiang Yan, Zhi Zhai, Xuefeng Chen
    Abstract:

    Cylindrical shell is a fundamental structure in the area of mechanical and architectural engineering. In the predesign stage, accurate analysis is a key step to guarantee the performance in application. Finite element method is a commonly used method in structural analysis. However, due to the limitations of interpolation functions, accuracy and efficiency are restricted. Wavelet finite element method is an advanced numerical method which uses Wavelet functions to replace the traditional polynomial function to discrete the solving variables. Daubechies, B-Spline Wavelet on the interval (BSWI) etc. have been used to construct the elements. However, they are mainly focused on the elements with one kind of variable. That is, only the displacement variable is interpolated directly and the generalized stress and strain are calculated second. Multivariable Wavelet finite element can deal with this problem, in which the three kinds of variables can be interpolated and solved directly, thus the calculation error can be avoiding. In this paper, the BSWI scaling functions are used to construct the Wavelet finite elements for cylindrical shell, including BSWI element with one kind of variables (BSWI-WFE), BSWI element with two kinds of variables (BSWI-TwWFE) and BSWI element with three kinds of variables (BSWI-ThWFE). Several numerical examples for cylindrical shell are provided to analyze the performance of the constructed elements and compared with each other to indicate superiority and efficiency.

  • mid frequency dynamic characteristics prediction of thin plate based on b Spline Wavelet on interval finite element method
    Applied Mathematical Modelling, 2018
    Co-Authors: Jia Geng, Xingwu Zhang, Xuefeng Chen, Chenxi Wang, Jiawei Xiang
    Abstract:

    Abstract Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c1 type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c1 type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c1 type WFEMs. On the other hand, the method combining c1 type B-Spline Wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.

  • predicting dynamic response of stiffened plate composite structures in a wide frequency domain based on composite b Spline Wavelet elements method cbwem
    International Journal of Mechanical Sciences, 2018
    Co-Authors: Jia Geng, Xingwu Zhang, Chenxi Wang, Xuefeng Chen
    Abstract:

    Abstract Due to the mid-frequency problem, the Hybrid Statistical Energy Analysis (SEA) / Traditional Finite Element Methods (TFEMs) methods still cannot provide the dynamic responses of the stiffened-plate composite structures in a wide frequency domain. The main reason is that all of the SEA and TFEMs cannot provide the reliable numerical solutions in the middle frequency domain when simulating the thin plate substructures. In order to solve the problem, this paper proposes the Composite B-Spline Wavelet Elements Method (CBWEM) based on the c1 type Wavelet plate and beam elements for modeling the stiffened-plate composite structures and predicting its dynamic responses in a wide frequency domain. Unfortunately, due to the complex interpolation functions and transformation matrices of these c1 type Wavelet elements, the existing numerical scheme to construct the constraint matrix will be invalid when modeling the coupling relationship between the c1 type Wavelet plate and beam elements. To solve the problem, this study deduces and gives the formulas of the new numerical scheme for constructing the constraint matrix and modeling the stiffened-plate composite structures based on the CBWEM. Besides, the numerical and experimental studies are carried out to verify the CBWEM, respectively. On the one hand, the numerical study displays that the proposed method can solve the mid-frequency problem and provide reliable dynamic responses in a wide frequency domain within an acceptable computational cost. On the other hand, the experimental study shows that the Central Processing Unit (CPU) time to predict the dynamic response in a wide frequency domain is less than 3.5 s only based on the proposed method and the personal computers, and the corresponding numerical solutions are in good agreement with the experimental results. Thus, we can easily conclude that the proposed method can be taken as one useful numerical technique to solve the mid-frequency problem and predict the dynamic responses of the stiffened-plate composite structures in a wide frequency domain.

  • analysis of laminated plates and shells using b Spline Wavelet on interval finite element
    International Journal of Structural Stability and Dynamics, 2017
    Co-Authors: Xingwu Zhang, Xuefeng Chen, Robert X Gao, Ruqiang Yan, Chuang Sun, Zhibo Yang
    Abstract:

    Composite materials, with characteristics of light weight and high strength, are useful in manufacturing. Therefore, precise design and analysis is the first key procedure in composite applications, improper analysis or use of composite materials may cause serious failures. In this paper, Wavelet finite element method (WFEM) based on B-Spline Wavelet on the interval (BSWI) is constructed for precise analysis of laminated plates and shells, which gives a guidance in design and application of composite structures. First, FEM formulations are derived from the generalized potential energy function based on the generalized variational principle and virtual work principle. Then, BSWI scaling functions are used as interpolation function to discretize the solving displacement field variables. At the same time, transformation matrix is constructed and used to translate the meaningless Wavelet coefficients into physical space. At last, the static analysis results can be obtained by solving the FEM formulations. Due to the excellent features of BSWI, such as multiresolution, multiscale, localization and excellent numerical approximation characteristics etc., BSWI-based FEM can achieve accurate and efficient analysis by comparing with traditional methods. In the end, the effectiveness of the constructed BSWI WFEM is verified through several numerical examples.

  • Analysis of shallow hyperbolic shell by different kinds of Wavelet elements based on B-Spline Wavelet on the interval
    Applied Mathematical Modelling, 2016
    Co-Authors: Xingwu Zhang, Xuefeng Chen, Hao Zuo, Jixuan Liu, Zhibo Yang
    Abstract:

    Abstract Shallow hyperbolic shell is a typical structure widely used in mechanical engineering and architectural engineering. Accurate structural analysis is a very important procedure before it is used in practical engineering. Wavelet finite element method (WFEM) is a new numerical analysis method which takes Wavelet functions to replace the polynomial functions in tradition FEM. Due to the excellent properties of Wavelet, WFEM can improve the calculation efficiency and reduce the computational time. However, traditional WFEM mainly focuses on accurate analysis of generalized displacement, generalized stress and generalized strain should be calculated secondly through displacement. Multivariable WFEM, including WFEM with two kinds of variables and WFEM with three kinds of variables, can independently interpolate the generalized displacement, stress and strain in one time, thus the calculation time is greatly reduced and the calculation precision can be improved significantly. In this paper, taking B-Spline Wavelet on the interval (BSWI) as interpolating function, the traditional BSWI element, BSWI element with two kinds of variables and BSWI element with three kinds of variables for the typical shell structure-shallow hyperbolic shell are constructed. Through bending and vibration analysis of shallow hyperbolic shell, the superiority of these three constructed elements is proved.

Xingwu Zhang - One of the best experts on this subject based on the ideXlab platform.

  • static and dynamic analysis of cylindrical shell by different kinds of b Spline Wavelet finite elements on the interval
    Engineering With Computers, 2020
    Co-Authors: Xingwu Zhang, Ruqiang Yan, Zhi Zhai, Xuefeng Chen
    Abstract:

    Cylindrical shell is a fundamental structure in the area of mechanical and architectural engineering. In the predesign stage, accurate analysis is a key step to guarantee the performance in application. Finite element method is a commonly used method in structural analysis. However, due to the limitations of interpolation functions, accuracy and efficiency are restricted. Wavelet finite element method is an advanced numerical method which uses Wavelet functions to replace the traditional polynomial function to discrete the solving variables. Daubechies, B-Spline Wavelet on the interval (BSWI) etc. have been used to construct the elements. However, they are mainly focused on the elements with one kind of variable. That is, only the displacement variable is interpolated directly and the generalized stress and strain are calculated second. Multivariable Wavelet finite element can deal with this problem, in which the three kinds of variables can be interpolated and solved directly, thus the calculation error can be avoiding. In this paper, the BSWI scaling functions are used to construct the Wavelet finite elements for cylindrical shell, including BSWI element with one kind of variables (BSWI-WFE), BSWI element with two kinds of variables (BSWI-TwWFE) and BSWI element with three kinds of variables (BSWI-ThWFE). Several numerical examples for cylindrical shell are provided to analyze the performance of the constructed elements and compared with each other to indicate superiority and efficiency.

  • mid frequency dynamic characteristics prediction of thin plate based on b Spline Wavelet on interval finite element method
    Applied Mathematical Modelling, 2018
    Co-Authors: Jia Geng, Xingwu Zhang, Xuefeng Chen, Chenxi Wang, Jiawei Xiang
    Abstract:

    Abstract Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c1 type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c1 type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c1 type WFEMs. On the other hand, the method combining c1 type B-Spline Wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.

  • predicting dynamic response of stiffened plate composite structures in a wide frequency domain based on composite b Spline Wavelet elements method cbwem
    International Journal of Mechanical Sciences, 2018
    Co-Authors: Jia Geng, Xingwu Zhang, Chenxi Wang, Xuefeng Chen
    Abstract:

    Abstract Due to the mid-frequency problem, the Hybrid Statistical Energy Analysis (SEA) / Traditional Finite Element Methods (TFEMs) methods still cannot provide the dynamic responses of the stiffened-plate composite structures in a wide frequency domain. The main reason is that all of the SEA and TFEMs cannot provide the reliable numerical solutions in the middle frequency domain when simulating the thin plate substructures. In order to solve the problem, this paper proposes the Composite B-Spline Wavelet Elements Method (CBWEM) based on the c1 type Wavelet plate and beam elements for modeling the stiffened-plate composite structures and predicting its dynamic responses in a wide frequency domain. Unfortunately, due to the complex interpolation functions and transformation matrices of these c1 type Wavelet elements, the existing numerical scheme to construct the constraint matrix will be invalid when modeling the coupling relationship between the c1 type Wavelet plate and beam elements. To solve the problem, this study deduces and gives the formulas of the new numerical scheme for constructing the constraint matrix and modeling the stiffened-plate composite structures based on the CBWEM. Besides, the numerical and experimental studies are carried out to verify the CBWEM, respectively. On the one hand, the numerical study displays that the proposed method can solve the mid-frequency problem and provide reliable dynamic responses in a wide frequency domain within an acceptable computational cost. On the other hand, the experimental study shows that the Central Processing Unit (CPU) time to predict the dynamic response in a wide frequency domain is less than 3.5 s only based on the proposed method and the personal computers, and the corresponding numerical solutions are in good agreement with the experimental results. Thus, we can easily conclude that the proposed method can be taken as one useful numerical technique to solve the mid-frequency problem and predict the dynamic responses of the stiffened-plate composite structures in a wide frequency domain.

  • analysis of laminated plates and shells using b Spline Wavelet on interval finite element
    International Journal of Structural Stability and Dynamics, 2017
    Co-Authors: Xingwu Zhang, Xuefeng Chen, Robert X Gao, Ruqiang Yan, Chuang Sun, Zhibo Yang
    Abstract:

    Composite materials, with characteristics of light weight and high strength, are useful in manufacturing. Therefore, precise design and analysis is the first key procedure in composite applications, improper analysis or use of composite materials may cause serious failures. In this paper, Wavelet finite element method (WFEM) based on B-Spline Wavelet on the interval (BSWI) is constructed for precise analysis of laminated plates and shells, which gives a guidance in design and application of composite structures. First, FEM formulations are derived from the generalized potential energy function based on the generalized variational principle and virtual work principle. Then, BSWI scaling functions are used as interpolation function to discretize the solving displacement field variables. At the same time, transformation matrix is constructed and used to translate the meaningless Wavelet coefficients into physical space. At last, the static analysis results can be obtained by solving the FEM formulations. Due to the excellent features of BSWI, such as multiresolution, multiscale, localization and excellent numerical approximation characteristics etc., BSWI-based FEM can achieve accurate and efficient analysis by comparing with traditional methods. In the end, the effectiveness of the constructed BSWI WFEM is verified through several numerical examples.

  • Analysis of shallow hyperbolic shell by different kinds of Wavelet elements based on B-Spline Wavelet on the interval
    Applied Mathematical Modelling, 2016
    Co-Authors: Xingwu Zhang, Xuefeng Chen, Hao Zuo, Jixuan Liu, Zhibo Yang
    Abstract:

    Abstract Shallow hyperbolic shell is a typical structure widely used in mechanical engineering and architectural engineering. Accurate structural analysis is a very important procedure before it is used in practical engineering. Wavelet finite element method (WFEM) is a new numerical analysis method which takes Wavelet functions to replace the polynomial functions in tradition FEM. Due to the excellent properties of Wavelet, WFEM can improve the calculation efficiency and reduce the computational time. However, traditional WFEM mainly focuses on accurate analysis of generalized displacement, generalized stress and generalized strain should be calculated secondly through displacement. Multivariable WFEM, including WFEM with two kinds of variables and WFEM with three kinds of variables, can independently interpolate the generalized displacement, stress and strain in one time, thus the calculation time is greatly reduced and the calculation precision can be improved significantly. In this paper, taking B-Spline Wavelet on the interval (BSWI) as interpolating function, the traditional BSWI element, BSWI element with two kinds of variables and BSWI element with three kinds of variables for the typical shell structure-shallow hyperbolic shell are constructed. Through bending and vibration analysis of shallow hyperbolic shell, the superiority of these three constructed elements is proved.

Zhibo Yang - One of the best experts on this subject based on the ideXlab platform.

  • analysis of laminated plates and shells using b Spline Wavelet on interval finite element
    International Journal of Structural Stability and Dynamics, 2017
    Co-Authors: Xingwu Zhang, Xuefeng Chen, Robert X Gao, Ruqiang Yan, Chuang Sun, Zhibo Yang
    Abstract:

    Composite materials, with characteristics of light weight and high strength, are useful in manufacturing. Therefore, precise design and analysis is the first key procedure in composite applications, improper analysis or use of composite materials may cause serious failures. In this paper, Wavelet finite element method (WFEM) based on B-Spline Wavelet on the interval (BSWI) is constructed for precise analysis of laminated plates and shells, which gives a guidance in design and application of composite structures. First, FEM formulations are derived from the generalized potential energy function based on the generalized variational principle and virtual work principle. Then, BSWI scaling functions are used as interpolation function to discretize the solving displacement field variables. At the same time, transformation matrix is constructed and used to translate the meaningless Wavelet coefficients into physical space. At last, the static analysis results can be obtained by solving the FEM formulations. Due to the excellent features of BSWI, such as multiresolution, multiscale, localization and excellent numerical approximation characteristics etc., BSWI-based FEM can achieve accurate and efficient analysis by comparing with traditional methods. In the end, the effectiveness of the constructed BSWI WFEM is verified through several numerical examples.

  • Analysis of shallow hyperbolic shell by different kinds of Wavelet elements based on B-Spline Wavelet on the interval
    Applied Mathematical Modelling, 2016
    Co-Authors: Xingwu Zhang, Xuefeng Chen, Hao Zuo, Jixuan Liu, Zhibo Yang
    Abstract:

    Abstract Shallow hyperbolic shell is a typical structure widely used in mechanical engineering and architectural engineering. Accurate structural analysis is a very important procedure before it is used in practical engineering. Wavelet finite element method (WFEM) is a new numerical analysis method which takes Wavelet functions to replace the polynomial functions in tradition FEM. Due to the excellent properties of Wavelet, WFEM can improve the calculation efficiency and reduce the computational time. However, traditional WFEM mainly focuses on accurate analysis of generalized displacement, generalized stress and generalized strain should be calculated secondly through displacement. Multivariable WFEM, including WFEM with two kinds of variables and WFEM with three kinds of variables, can independently interpolate the generalized displacement, stress and strain in one time, thus the calculation time is greatly reduced and the calculation precision can be improved significantly. In this paper, taking B-Spline Wavelet on the interval (BSWI) as interpolating function, the traditional BSWI element, BSWI element with two kinds of variables and BSWI element with three kinds of variables for the typical shell structure-shallow hyperbolic shell are constructed. Through bending and vibration analysis of shallow hyperbolic shell, the superiority of these three constructed elements is proved.

  • the analysis of curved beam using b Spline Wavelet on interval finite element method
    Shock and Vibration, 2014
    Co-Authors: Zhibo Yang, Xuefeng Chen, Jie Zhang
    Abstract:

    A B-Spline Wavelet on interval (BSWI) finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch) are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct Wavelet-based elements. Different from the process of the direct Wavelet addition in the other Wavelet numerical methods, the element displacement field represented by the coefficients of Wavelets expansions is transformed from Wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies Wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.

  • free vibration and buckling analysis of plates using b Spline Wavelet on the interval mindlin element
    Applied Mathematical Modelling, 2013
    Co-Authors: Zhibo Yang, Xuefeng Chen, Xingwu Zhang
    Abstract:

    Abstract A finite element method (FEM) of B-Spline Wavelet on the interval (BSWI) is used in this paper to solve the free vibration and buckling problems of plates based on Reissner–Mindlin theory. By aid of the high accuracy of B-Spline functions approximation for structural analysis, the proposed method could obtain a fast convergence and a satisfying numerical accuracy with fewer degrees of freedoms (DOF). The numerical examples demonstrate that the present BSWI method achieves the high accuracy compared to the exact solution and others existing approaches in the literatures. The BSWI finite element has potential to be used as a numerical method in analysis and design.

  • vibration analysis of curved shell using b Spline Wavelet on the interval bswi finite elements method and general shell theory
    Cmes-computer Modeling in Engineering & Sciences, 2012
    Co-Authors: Zhibo Yang, Xuefeng Chen, Huihui Miao
    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 hy- perbolic 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 com- bine the accuracy of Wavelet-based elements approximation and the character of B-Spline functions for structural analysis. Different from the flat shell elements, the curved shell elements obtain a better geometrical fitting property in idealiz- ing the practical curved structures. This paper focuses on the dynamic analysis of shell. The study covers wide combinations of boundaries such as cantilever, sim- ply supported and clamped boundary. Numerical results have been established to validate the efficiency and accuracy of the presented elements through comparison with published data from the open literature and some commercial finite element method software.

Zhong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • translation invariant ri Spline Wavelet and its application on de noising
    International Journal of Information Technology and Decision Making, 2006
    Co-Authors: Zhong Zhang, Hiroshi Toda, H Fujiwara, Fuji Ren
    Abstract:

    Wavelet Shrinkage using DWT has been widely used in de-noising although DWT has a translation variance problem. In this study, we solve this problem by using the translation invariant DWT. For this purpose, we propose a new complex Wavelet, the Real-Imaginary Spline Wavelet (RI-Spline Wavelet). We also propose the Coherent Dual-Tree algorithm for the RI-Spline Wavelet and extend it to the 2-Dimensional. Then we apply this translation invariant RI-Spline Wavelet for translation invariant de-noising. Experimental results show that our method, when applied to ECG data, the medical image and the textile surface inspection can obtain better de-noising results than that of conventional Wavelet Shrinkage.

  • nonstationary signal analysis using the ri Spline Wavelet
    Computer-Aided Engineering, 2006
    Co-Authors: Zhong Zhang, Satoshi Horihata, Hiroshi Toda, Tetsuo Miyake
    Abstract:

    In our first report, we have proposed a complex type Wavelet, the Real-Imaginary Spline Wavelet (RI-Spline Wavelet) for the continuous Wavelet transform and demonstrated the advantages of our approach. In this study, we develop our RI-Spline Wavelet for the Discrete Wavelet Transform (DWT) that uses a fast algorithm based on Multi-resolution analysis. The DWT has a translation variance problem, so it can not catch features of the signals exactly although it has been widely used in signal analysis. In order to overcome this translation variance problem, we first develop a Complex Discrete Wavelet Transform (CDWT) using the RI-Spline Wavelet and propose the Coherent Dual-Tree algorithm for the RI-Spline Wavelet without increasing the computational cost very much. Then we apply this translation invariant CDWT to translation invariant de-noising. Experimental results show that our method, when applied to ECG data and music data, can obtain better de-noising results than conventional Wavelet Shrinkage.

  • signal processing using translation invariant ri Spline Wavelet
    Systems Man and Cybernetics, 2004
    Co-Authors: Zhong Zhang, H Fujiwara, Fuji Ren
    Abstract:

    De-noising using Wavelet shrinkage has a translation variance problem, which we solve by using the translation invariant DWT. For this purpose, we propose a new complex Wavelet, the real-imaginary Spline Wavelet (RI-Spline Wavelet). We also propose the coherent dual-tree algorithm for the RI-Spline Wavelet without increasing the computational cost very much. Then we apply this translation invariant RI-Spline Wavelet for translation invariant denoising. Experimental results show that our method, when applied to ECG data and a music signal, can obtain better de-noising results than Wavelet shrinkage.

  • a new complex Wavelet transform by using ri Spline Wavelet
    International Conference on Acoustics Speech and Signal Processing, 2004
    Co-Authors: Zhong Zhang, Hiroshi Toda, H Fujiwara, H Kawabata
    Abstract:

    We propose a new complex Wavelet, the RI-Spline Wavelet, which is constructed using Spline Wavelets for dual-tree DWT. In the RI-Spline Wavelet, the real and imaginary components become an approximate Hilbert pair to each other. Then we propose a new dual-tree algorithm which uses an interpolation method for providing a half-sample-delay between the two filters of the trees. Finally, we experimentally show that the translation invariance, which can not be obtained by the ordinary DWT, is obtained by RI-Spline Wavelet.

Jiawei Xiang - One of the best experts on this subject based on the ideXlab platform.

  • mid frequency dynamic characteristics prediction of thin plate based on b Spline Wavelet on interval finite element method
    Applied Mathematical Modelling, 2018
    Co-Authors: Jia Geng, Xingwu Zhang, Xuefeng Chen, Chenxi Wang, Jiawei Xiang
    Abstract:

    Abstract Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c1 type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c1 type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c1 type WFEMs. On the other hand, the method combining c1 type B-Spline Wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.

  • static and vibration analysis of thin plates by using finite element method of b Spline Wavelet on the interval
    Structural Engineering and Mechanics, 2007
    Co-Authors: Jiawei Xiang, Xuefeng Chen
    Abstract:

    A finite element method (FEM) of B-Spline Wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-Spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

  • the construction of Wavelet based truncated conical shell element using b Spline Wavelet on the interval
    Acta Mechanica Solida Sinica, 2006
    Co-Authors: Jiawei Xiang, Xuefeng Chen
    Abstract:

    Based on B-Spline Wavelet on the interval (BSWI), two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slope-deformation interpolation. In the construction of Wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct Wavelets adding in the Wavelet Galerkin method, the elemental displacement field represented by the coefficients of Wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-Spline function approximation and various Wavelet-based elements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.

  • identification of a crack in a beam based on the finite element method of a b Spline Wavelet on the interval
    Journal of Sound and Vibration, 2006
    Co-Authors: Jiawei Xiang, Xuefeng Chen
    Abstract:

    The model-based forward and inverse problems in the diagnosis of structural crack location and size by using the finite element method of a B-Spline Wavelet on the interval (FEM BSWI) were studied. First the crack and uncracked elements of BSWI were built to solve the forward problem. The first three frequencies influencing functions of normalized crack location and size are approximated by means of surface-fitting techniques. Then the first three measured natural frequencies are employed as inputs of the functions. The intersection of the three frequencies contour lines predicted the normalized crack location and size. Both the numerical and experimental studies verified the validity of the BSWI elements in solving crack singular problems with high performance.

  • the construction of plane elastomechanics and mindlin plate elements of b Spline Wavelet on the interval
    Finite Elements in Analysis and Design, 2006
    Co-Authors: Jiawei Xiang, Xuefeng Chen
    Abstract:

    Based on two-dimensional tensor product B-Spline Wavelet on the interval (BSWI), a class of CO type plate elements is constructed to solve plane elastomechanics and moderately thick plate problems. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to form the shape functions and construct BSWI elements. Unlike the process of direct Wavelets adding in the previous work, the elemental displacement field represented by the coefficients of Wavelets expansions is transformed into edges and internal modes via the constructed transformation matrix in this paper. The method combines the versatility of the conventional finite element method (FEM) with the accuracy of B-Spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the closed-form or traditional FEM solutions.