scholarly journals Wavelet Element Modelling for Inviscid Fluid–Solid Coupling Problem based on Partitioned Approach

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3699
Author(s):  
Zhi-Bo Yang ◽  
Hao-Qi Li ◽  
Bai-Jie Qiao ◽  
Xue-Feng Chen
Keyword(s):  
Inviscid Fluid ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Partitioned Approach ◽  
Complex Shapes ◽  
Jacobi Iteration ◽  
Spatial Domains ◽  
Numerical Formulation ◽  
Alternative Choice ◽  
Element Method

To provide a simple numerical formulation based on fixed grids, a wavelet element method for fluid–solid modelling is introduced in this work. Compared with the classical wavelet finite element method, the presented method can potentially handle more complex shapes. Considering the differences between the solid and fluid regions, a damping-like interface based on wavelet elements is designed, in order to ensure consistency between the two parts. The inner regions are constructed with the same wavelet function in space. In the time and spatial domains, a partitioned approach based on Jacobi iteration is combined with the pseudo-parallel calculation method. Numerical convergence analyses show that the method can serve as an alternative choice for fluid–solid coupling modelling.

Wavelet Finite Element Method Analysis of Bending Plate Based on Hermite Interpolation

2013 ◽  
Vol 389 ◽  
pp. 267-272 ◽  
Author(s):  
Peng Shen ◽  
Yu Min He ◽  
Zhi Shan Duan ◽  
Zhong Bin Wei ◽  
Pan Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Hermite Interpolation ◽  
Energy Functional ◽  
Field Function ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Crack Problems ◽  
Element Method

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

scholarly journals Wave Motion Analysis in Plane via Hermitian Cubic Spline Wavelet Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaofeng Xue ◽  
Xinhai Wang ◽  
Zhen Wang ◽  
Wei Xue
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Motion Analysis ◽  
Wave Motion ◽  
Shape Functions ◽  
Scale Functions ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Plane Element ◽  
Element Method

A plane Hermitian wavelet finite element method is presented in this paper. Wave motion can be used to analyze plane structures with small defects such as cracks and obtain results. By using the tensor product of modified Hermitian wavelet shape functions, the plane Hermitian wavelet shape functions are constructed. Scale functions of Hermitian wavelet shape functions can replace the polynomial shape functions to construct new wavelet plane elements. As the scale of the shape functions increases, the precision of the new wavelet plane element will be improved. The new Hermitian wavelet finite element method which can be used to simulate wave motion analysis can reveal the law of the wave motion in plane. By using the results of transmitted and reflected wave motion, the cracks can be easily identified in plane. The results show that the new Hermitian plane wavelet finite element method can use the fewer elements to simulate the plane structure effectively and accurately and detect the cracks in plane.

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