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THE CONSTRUCTION OF wavelet-bASED TRUNCATED CONICAL SHELL ELEMENT USING b-spline wavelet on the interval

Acta Mechanica Solida Sinica 2006年第4期19卷 316-326页

作者： Xiang Jiawei He Zhengjia Chen Xuefeng School of Mechantronic Engineering Guilin University of Electronic Technology Guilin 541004 China School of Mechanical Engineering Xi＇an Jiaotong University The State Key Laboratory for Manufacturing Systems Engineering Xi ＇an 710049 China

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 slopedeformation 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.

关键词： b-spline wavelet on the interval finite element method axisymmetric problem truncated conical shell element

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b-spline wavelet on interval Finite Element Method for Static and Vibration Analysis of Stiffened Flexible Thin Plate

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Computers, Materials & Continua 2016年第4期52卷 53-71页

作者： Xing Wei Wen Chen bin Chen bin Chen2 bin Chen3 bin Chen4 State Key Laboratory for Manufacturing System Engineering School of Mechanical EngineeringXi’an Jiaotong UniversityXi’an 710049PR China Department of Mechanical and Aerospace Engineering Case Western Reserve UniversityCleveland Ohio 44106USA School of Instrument Science and Engineering Southeast UniversityNanjing 210096PR China

A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are *** means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived ***,the scaling functions of the b-spline wavelet on the interval(bSWI)are introduced to discrete the solving field variables instead of conventional polynomial ***,the corresponding two problems can be resolved following the traditional finite element *** are some advantages of the constructed elements in structural *** to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the bSWI,the precise and efficient analysis can be ***,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is *** order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.

关键词： b-spline wavelet on the interval wavelet finite element method Stiffened plate bending analysis Vibration analysis

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Construction and Application of Multivariable Finite Element for Flat Shell Analysis

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Acta Mechanica Solida Sinica 2018年第4期31卷 391-404页

作者： Xingwu Zhang Yanfei He Robert X. Gao Jia Geng Xuefeng Chen Jiawei Xiang State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University Xi'an 710049 China School of Mechanical Engineering Xi ' an Jiaotong University Xi ' an 710049 China Department of Mechanical Engineering Case Western Reserve University Cleveland OH 44106 USA Zhejiang Provincial Key Laboratory of Laser Processing Robot/Key Laboratory of Laser Precision Processing & Detection Wenzhou University Wenzhou 325035 China

based on b-spline wavelet on the interval （bSWI） and the multivariable generalized variational principle, the multivariable wavelet finite element for flat shell is constructed by combining the elastic plate element and the Mindlin plate element together. First, the elastic plate element formulation is derived from the generalized potential energy function. Due to its excellent numerical approximation property, bSWI is used as the interpolation function to separate the solving field variables. Second, the multivariable wavelet Mindlin plate element is deduced and constructed according to the multivariable generalized variational principle and bSWI. Third, by following the displacement compatibility requirement and the coordinate transformation method, the multivariable wavelet finite element for fiat shell is constructed. The novel advantage of the constructed element is that the solving precision and efficiency can be improved because the generalized displacement field variables and stress field variables are interpolated and solved independently. Finally, several numerical examples including bending and vibration analyses are given to verify the constructed element and method.

关键词： b-spline wavelet on the interval Elastic plate Mindlin plate Flat shell Multivariable

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wavelet-based boundary Element Method for Calculating the band Structures of Two-Dimensional Phononic Crystals

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Acta Mechanica Solida Sinica 2021年第5期34卷 687-705页

作者： Qi Wei Xingfu Ma Jiawei Xiang College of Mechanical and Electrical Engineering Wenzhou UniversityWenzhou325035China

A wavelet-based boundary element method is employed to calculate the band structures of two-dimensional phononic crystals,which are composed of square or triangular lattices with scatterers of arbitrary cross *** the aid of structural periodicity,the boundary integral equations of both the scatterer and the matrix are discretized in a unit *** make the curve boundary compatible,the second-order scaling functions of the b-spline wavelet on the interval are used to approximate the geometric boundaries,while the boundary variables are interpolated by scaling functions of arbitrary *** any given angular frequency,an effective technique is given to yield matrix values related to the boundary ***,combining the periodic boundary conditions and interface conditions,linear eigenvalue equations related to the bloch wave vector are *** numerical examples illustrate the superior performance of the proposed method by comparing with the conventional bEM.

关键词： wavelet-based boundary element method b-spline wavelet on the interval Phononic crystal band structure

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THE ANALYSIS OF SHALLOW SHELLS bASED ON MULTIVARIAbLE wavelet FINITE ELEMENT METHOD

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Acta Mechanica Solida Sinica 2011年第5期24卷 450-460页

作者： Xingwu Zhang Xuefeng Chen Zhengjia He Zhibo Yang State Key Laboratory for Manufacturing System Engineering School of Mechanical Engineering Xi＇an Jiaotong University Xi＇an 710049 China

based on the generalized variational principle and b-spline wavelet on the interval （bSWI）, the multivariable bSWI elements with two kinds of variables （TbSWI） for hyperboloidal shell and open cylindrical shell are constructed in this paper. Different from the traditional method, the present one treats the generalized displacement and stress as independent variables. So differentiation and integration are avoided in calculating generalized stress and thus the precision is improved. Furthermore, compared with commonly used Daubechies wavelet, bSWI has explicit expression and excellent approximation property and thus further guarantee satisfactory results. Finally, the efficiency of the constructed multivariable shell elements is validated through several numerical examples.

关键词： multivariable b-spline wavelet on the interval hyperboloidal shell open cylindrical shell

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