Static and vibration analysis of thin plates by using finite element method of B-spline wavelet on the interval

2007 ◽  
Vol 25 (5) ◽  
pp. 613-629 ◽  
Author(s):  
Jiawei Xiang ◽  
Zhengjia He ◽  
Yumin He ◽  
Xuefeng Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Thin Plates ◽  
Spline Wavelet ◽  
B Spline ◽  
Element Method

B-Spline Wavelet-Based Finite Element Vibration Analysis of Composite Pipes with Internal Surface Defects of Different Geometries

2017 ◽  
Vol 17 (04) ◽  
pp. 1750051 ◽  
Author(s):  
Wasiu A. Oke ◽  
Yehia A. Khulief
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Surface Defects ◽  
Internal Surface ◽  
Spline Wavelet ◽  
B Spline ◽  
Composite Pipe ◽  
Composite Pipes ◽  
Element Method

The vibration analysis of composite pipes with internal wall defects due to erosion-induced surface degradation is investigated. The surface defects are treated as discontinuities. The geometry of the discontinuity is permitted to vary within the cross-section both in the angular and radial directions, and to occupy any length of the pipe span. A B-spline wavelet-based finite element method (BWFEM) that takes advantage of the localization properties of wavelets is invoked; thus utilizing its effectiveness in modeling of crack problems and local damages. The composite pipe was treated as beam elements that obey the Euler–Bernoulli beam theory. Unlike the conventional finite element method (FEM), the developed BWFEM uses fewer elements without compromising the accuracy. Numerical simulations are performed to demonstrate the accuracy and efficiency of the developed element through comparison with available results in the literature, as well as results obtained using ANSYS. Some benchmark solutions are obtained for the composite pipe with internal surface defects of different geometries.

scholarly journals About the B-spline wavelet discrete-continual finite element method of the local plate analysis

Vestnik MGSU ◽  
2021 ◽  
pp. 666-675
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Taymuraz B. Kaytukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Element Approximation ◽  
Plate Material ◽  
Basic Direction ◽  
Spline Wavelet ◽  
B Spline ◽  
Plate Analysis ◽  
Element Method

Introduction. This distinctive paper addresses the local semi-analytical solution to the problem of plate analysis. Isotropic plates featuring the regularity (constancy) of physical and geometric parameters (modulus of elasticity of the plate material, Poisson’s ratio of the plate material, dimensions of the cross section of the plate) along one direction (dimension) are under consideration. This direction is conventionally called the basic direction. Materials and methods. The B-spline wavelet discrete-continual finite element method (DCFEM) is used. The initial operational formulation of the problem was constructed using the theory of distribution and the so-called method of extended domain, proposed by Prof. Alexander B. Zolotov. Results. Some relevant issues of construction of normalized basis functions of the B-spline are considered; the technique of approximation of corresponding vector functions and operators within DCFEM is described. The problem remains continual if analyzed along the basic direction, and its exact analytical solution can be obtained, whereas the finite element approximation is used in combination with a wavelet analysis apparatus in respect of the non-basic direction. As a result, we can obtain a discrete-continual formulation of the problem. Thus, we have a multi-point (in particular, two-point) boundary problem for the first-order system of ordinary differential equations with constant coefficients. A special correct analytical method of solving such problems was developed, described and verified in the numerous papers of the co-authors. In particular, we consider the simplest sample analysis of a plate (rectangular in plan) fixed along the side faces exposed to the influence of the load concentrated in the center of the plate. Conclusions. The solution to the verification problem obtained using the proposed version of wavelet-based DCFEM was in good agreement with the solution obtained using the conventional finite element method (the corresponding solutions were constructed with and without localization; these solutions almost completely coincided, while the advantages of the numerical-analytical approach were quite obvious). It is shown that the use of B-splines of various degrees within wavelet-based DCFEM leads to a significant reduction in the number of unknowns.

101 On fracture analysis using B-spline wavelet finite element method

2008 ◽  
Vol 2008.46 (0) ◽  
pp. 1-2
Author(s):  
Yuichi SUGIMOTO ◽  
Satoyuki TANAKA ◽  
Hiroshi OKADA ◽  
Masahiko FUJIKUBO ◽  
Shigenobu OKAZAWA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Analysis ◽  
Spline Wavelet ◽  
B Spline ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Element Method

Free Vibration Analysis of Frame Structures Using BSWI Method

2008 ◽  
Author(s):  
Farhang Daneshmand ◽  
Abdolaziz Abdollahi ◽  
Mehdi Liaghat ◽  
Yousef Bazargan Lari
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Frame Structures ◽  
Shape Functions ◽  
Element Analysis ◽  
B Spline ◽  
Multi Level ◽  
Element Method

Vibration analysis for complicated structures, or for problems requiring large numbers of modes, always requires fine meshing or using higher order polynomials as shape functions in conventional finite element analysis. Since it is hard to predict the vibration mode a priori for a complex structure, a uniform fine mesh is generally used which wastes a lot of degrees of freedom to explore some local modes. By the present wavelets element approach, the structural vibration can be analyzed by coarse mesh first and the results can be improved adaptively by multi-level refining the required parts of the model. This will provide accurate data with less degrees of freedom and computation. The scaling functions of B-spline wavelet on the interval (BSWI) as trial functions that combines the versatility of the finite element method with the accuracy of B-spline functions approximation and the multiresolution strategy of wavelets is used for frame structures vibration analysis. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly 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 via the corresponding transformation matrix. To verify the proposed method, the vibrations of a cantilever beam and a plane structures are studied in the present paper. The analyses and results of these problems display the multi-level procedure and wavelet local improvement. The formulation process is as simple as the conventional finite element method except including transfer matrices to compute the coupled effect between different resolution levels. This advantage makes the method more competitive for adaptive finite element analysis. The results also show good agreement with those obtained from the classical finite element method and analytical solutions.

Modal Analysis of Cracked Plate Using Interval B-Spline Wavelet Finite Element Method

2011 ◽  
Vol 199-200 ◽  
pp. 1287-1291
Author(s):  
Hui Fen Peng ◽  
Guang Wei Meng ◽  
Li Ming Zhou ◽  
Zhao Long Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
Mode Shapes ◽  
Plate Element ◽  
Spline Wavelet ◽  
B Spline ◽  
Cracked Plate ◽  
Wavelet Finite Element ◽  
Element Method

Aiming at the defects in describing stress field near the crack tip with traditional finite element method (TFEM), a new finite element method based on interval B-Spline wavelet (IBSW) is put forward, the displacement interpolation functions of plate element are constructed by using the scaling functions of IBSW, finite element model of cracked plate based on IBSW is established, and the stiffness matrixes of plate element is derived. The first four natural frequencies and mode shapes of the cracked plate are obtained by using interval B-Spline wavelet finite element (IBSWFE). Comparison of the calculated results with those by ANSYS shows that IBSWFE method can get higher calculation precision with less elements in dealing with engineering singularity problems.

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