scholarly journals Enrichment of the Finite Element Method With the Reproducing Kernel Particle Method

1997 ◽  
Vol 64 (4) ◽  
pp. 861-870 ◽  
Author(s):  
Wing Kam Liu ◽  
R. A. Uras ◽  
Y. Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Computational Procedure ◽  
Reproducing Kernel Particle Method ◽  
The Finite Element Method ◽  
Window Functions ◽  
Reproducing Kernel Particle ◽  
Element Method

The reproducing kernel particle method (RKPM) has attractive properties in handling high gradients, concentrated forces, and large deformations where other widely implemented methodologies fail. In the present work, a multiple field computational procedure is devised to enrich the finite element method with RKPM, and RKPM with analytical functions. The formulation includes an interaction term that accounts for any overlap between the fields, and increases the accuracy of the computational solutions in a coarse mesh or particle grid. By replacing finite element method shape Junctions at selected nodes with higher-order RKPM window functions, RKPM p-enrichment is obtained. Similarly, by adding RKPM window functions into a finite element method mesh, RKPM hp-enrichment is achieved analogous to adaptive refinement. The fundamental concepts of the multiresolution analysis are used to devise an adaptivity procedure.

scholarly journals Numerical Simulation of Hypervelocity Impact FEM-SPH Algorithm Based on Large Deformation of Material

2016 ◽  
Author(s):  
Aimin Yang ◽  
Jinze Li ◽  
Hengheng Qu ◽  
Yuhang Pan ◽  
Yanhong Kang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Particle Method ◽  
The Finite Element Method ◽  
Smoothed Particle ◽  
Sph Algorithm ◽  
Coupling Algorithm ◽  
Large Deformation Problems ◽  
Element Method

In this paper, we first discuss the research status and application progress of the finite element method and the smoothed particle method. By analyzing the advantages of the smoothed particle method and the finite element method, a new coupling algorithm, namely FEM-SPH algorithm, is proposed. By the method of comparison, it shows that finite element method and SPH method in the simulation of large deformation problems each have advantages and disadvantages, the finite element method smoothed particle coupling algorithm is effective to achieve the performance of high computational efficiency and can naturally simulate large deformation problems across. In the process of calculation, the large deformation unit can be freely into an algorithm to facilitate the calculation accuracy and efficiency of three methods of numerical simulation. Through the study found, FEM-SPH algorithm not only overcome the defect of smooth particle tensile instability, but also overcomes the problem of low efficiency of finite element computation. To further test the FEM-SPH algorithm has advantages in the practical engineering, we have carried out the actual test to the example of the super high speed collision, concluded that, since the target of most of the computational domain is always finite element, smoothed particle focused only in contact with the projectile and target of local area, particle number is not much, the whole calculation process just ten minutes, computational efficiency has been greatly improved, at the same time in the simulation of large deformation, the advantage is very obvious .This provides a criterion for the actual project, depending on the specific material deformation mode and choose a more appropriate conversion algorithm.

Multiresolution Reproducing Kernel Particle Methods in Acoustics

1997 ◽  
Vol 05 (01) ◽  
pp. 71-94 ◽  
Author(s):  
R. A. Uras ◽  
C.-T. Chang ◽  
Y. Chen ◽  
W. K. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Reproducing Kernel ◽  
Particle Methods ◽  
Wave Number ◽  
Frequency Range ◽  
Frequency Wave ◽  
Reproducing Kernel Particle ◽  
Element Method

In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention in order to give a realistic representation of the physics. As a powerful tool, the finite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-finite elements and/or hp-finite elements are employed. The Reproducing Kernel Particle Methods (RKPM) are emerging as an effective alternative due to the absence of a mesh and the ability to analyze a specific frequency range. In this study, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The interpolation functions consist of spline functions with a built-in window which permits translation as well as dilation. A variation in the size of the window implies a geometrical refinement and allows the filtering of the desired frequency range. An adaptivity similar to hp-finite element method is obtained through the choice of an optimal dilation parameter. The analysis of the wave equation shows the effectiveness of this approach. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. A similar methodology is also developed for the Timoshenko beam.

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