Improvement of numerical modeling in the solution of static and transient dynamic problems using finite element method based on spherical Hankel shape functions

2018 ◽  
Vol 115 (10) ◽  
pp. 1241-1265 ◽  
Author(s):  
S. Hamzehei-Javaran ◽  
S. Shojaee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Dynamic Problems ◽  
Shape Functions ◽  
Transient Dynamic ◽  
Element Method

Numerical modeling of shallow magma intrusions with finite element method

2017 ◽  
Vol 333-334 ◽  
pp. 53-65 ◽  
Author(s):  
Tielin Chen ◽  
Shaozhen Cheng ◽  
Qian Fang ◽  
Cheng Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Element Method

A Four-Noded Triangular (Tr4) Element for Solid Mechanics Problems with Curved Boundaries

2019 ◽  
Vol 17 (01) ◽  
pp. 1844003 ◽  
Author(s):  
Jun Hong Yue ◽  
Guirong Liu ◽  
Ruiping Niu ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solid Mechanics ◽  
Accurate Approximation ◽  
Shape Functions ◽  
Curved Boundaries ◽  
Triangular Elements ◽  
Complicated Geometry ◽  
Element Method ◽  
Physics Problems

Linear triangular elements with three nodes (Tr3) were the earliest, simplest and most widely used in finite element (FE) developed for solving mechanics and other physics problems. The most important advantages of the Tr3 elements are the simplicity, ease in generation, and excellent adaptation to any complicated geometry with straight boundaries. However, it cannot model well the geometries with curved boundaries, which is known as one of the major drawbacks. In this paper, a four-noded triangular (Tr4) element with one curved edge is first used to model the curved boundaries. Two types of shape functions of Tr4 elements have been presented, which can be applied to finite element method (FEM) models based on the isoparametric formulation. FE meshes can be created with mixed linear Tr3 and the proposed Tr4 (Tr3-4) elements, with Tr3 elements for interior and Tr4 elements for the curved boundaries. Compared to the pure FEM-Tr3, the FEM-Tr3-4 can significantly improve the accuracy of the solutions on the curved boundaries because of accurate approximation of the curved boundaries. Several solid mechanics problems are conducted, which validate the effectiveness of FEM models using mixed Tr3-4 meshes.

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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