The construction of plane elastomechanics and Mindlin plate elements of B-spline wavelet on the interval

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.

[1]  A. Cohen.  Numerical Analysis of Wavelet Methods , 2003 .

[2]  Prodyot K. Basu,et al.  Higher-order modeling of continua by finite-element, boundary-element, meshless, and wavelet methods , 2003 .

[3]  Claudio Canuto,et al.  The wavelet element method. Part I: Construction and analysis. , 1997 .

[4]  W. H. Chen,et al.  A spline wavelets element method for frame structures vibration , 1995 .

[5]  C. Chui,et al.  On solving first-kind integral equations using wavelets on a bounded interval , 1995 .

[6]  Long Yu-qiu,et al.  A universal method for including shear deformation in thin plate elements , 1992 .

[7]  Song Cen,et al.  A new twelve DOF quadrilateral element for analysis of thick and thin plates , 2001 .

[8]  Zheng Xiaojing,et al.  Applications of wavelet galerkin fem to bending of beam and plate structures , 1998 .

[9]  Peixiang He,et al.  Bending analysis of rectangular moderately thick plates using spline finite element method , 1995 .

[10]  Wolfgang Dahmen,et al.  Stable multiscale bases and local error estimation for elliptic problems , 1997 .

[11]  Zhengjia He,et al.  The construction of wavelet finite element and its application , 2004 .

[12]  Claudio Canuto,et al.  The wavelet element method. Part II: Realization and additional features in 2D and 3D , 1997 .

[13]  Zhengjia He,et al.  A study of the construction and application of a Daubechies wavelet-based beam element , 2003 .

[14]  Silvia Bertoluzza,et al.  Wavelet Methods for the Numerical Solution of Boundary Value Problems on the Interval , 1994 .

[15]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[16]  Ray W. Clough,et al.  Improved numerical integration of thick shell finite elements , 1971 .

[17]  Demetres Briassoulis,et al.  On the basics of the shear locking problem of C0 isoparametric plate elements , 1989 .

[18]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[19]  E. Quak,et al.  Decomposition and Reconstruction Algorithms for Spline Wavelets on a Bounded Interval , 1994 .

[20]  C. Chui,et al.  Wavelets on a Bounded Interval , 1992 .

[21]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[22]  W. H. Chen,et al.  Extension of spline wavelets element method to membrane vibration analysis , 1996 .

[23]  Andrew J. Kurdila,et al.  Triangular wavelet based finite elements via multivalued scaling equations , 1995 .

[24]  C. Chui,et al.  Wavelets : theory, algorithms, and applications , 1994 .