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.

scholarly journals Multiresolution Reproducing Kernel Particle Methods in Acoustic Problems

1995 ◽  
Author(s):  
W. K. Liu ◽  
C. T. Chang ◽  
Y. Chen ◽  
R. A. Uras
Keyword(s):  
Finite Elements ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Particle Methods ◽  
Wave Number ◽  
Frequency Range ◽  
Frequency Wave ◽  
Realistic Representation ◽  
Reproducing Kernel Particle ◽  
Complex Phenomena

Abstract In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention for 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 elimination of a mesh, and the ability to analyze a specific frequency range. Additionally, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The interpolation functions consist of spline functions with built-in window. A variation in the size of the window implies a geometrical refinement, and allows the filtering of the desired frequency range. Preliminary 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.

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.

A Numerical Proof-Test of Finite Element Method to Simulate Wave Propagation in Ground Soil

2012 ◽  
Vol 170-173 ◽  
pp. 3338-3344
Author(s):  
Xia Xin Tao ◽  
Xin Zheng ◽  
Fu Tong Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Length ◽  
Mesh Size ◽  
Harmonic Excitation ◽  
Wave Number ◽  
Calculation Error ◽  
Frequency Wave ◽  
Element Method

A numerical case study is presented in this paper to demonstrate the feasibility of a finite element method with artificial boundary condition to simulate the wave in 3D ground soil. An unit centralized harmonic excitation at surface is adopted with four frequencies. The calculated vibration amplitudes are compared with the corresponding results by dynamic Green Function in frequency-wave number domain. The result shows a clear calculation error phenomena that the smaller mesh adopted, the smaller error is for a given frequency, and the lower frequency excited so the smaller error is for a given mesh size. A preliminary suggestion is presented as that the maximum mesh size of a 3D discrete grid must be no larger than 1/25 of the minimum wave length.

A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number

2017 ◽  
Vol 22 (1) ◽  
pp. 133-156 ◽  
Author(s):  
Yu Du ◽  
Zhimin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Phase Error ◽  
Three Dimensions ◽  
Wave Number ◽  
Weak Galerkin ◽  
High Wave Number ◽  
Large Wave ◽  
Element Method

AbstractWe study the error analysis of the weak Galerkin finite element method in [24, 38] (WG-FEM) for the Helmholtz problem with large wave number in two and three dimensions. Using a modified duality argument proposed by Zhu and Wu, we obtain the pre-asymptotic error estimates of the WG-FEM. In particular, the error estimates with explicit dependence on the wave numberkare derived. This shows that the pollution error in the brokenH1-norm is bounded byunder mesh conditionk7/2h2≤C0or (kh)2+k(kh)p+1≤C0, which coincides with the phase error of the finite element method obtained by existent dispersion analyses. Herehis the mesh size,pis the order of the approximation space andC0is a constant independent ofkandh. Furthermore, numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.

The Application of a Finite Element Method to the Evaluation of oil Whirl Characteristics

1974 ◽  
Vol 16 (2) ◽  
pp. 101-108 ◽  
Author(s):  
P. Shelly ◽  
C. Ettles
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Parabolic Type ◽  
Pressure Profile ◽  
Combined Effects ◽  
Axial Pressure ◽  
Oil Whirl ◽  
Element Method

A method using finite elements for the whirl analysis of plain bearings is outlined. The special properties of an exponentially shaped element are linked to a parabolic type of approximation for the axial pressure profile. The method is developed and applied to the prediction of whirl paths of a heavy rotor operating both in the horizontal and vertical modes. Several locus paths are presented to show the separate and combined effects of rotor unbalance and unidirectional loading over a range of rotational speeds.

Teaching Electromagnetics through Finite Elements. Part I: The Rationale

1988 ◽  
Vol 25 (1) ◽  
pp. 33-49 ◽  
Author(s):  
S. Ratnajeevan H. Hoole
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Special Solution ◽  
The Finite Element Method ◽  
Solution Methods ◽  
Element Method

The rationale for teaching undergraduate electromagnetics partly through the finite element method, is put forward. Properly presented, the finite element method, easily within the ken of the engineering undergraduate, promotes clarity and helps to replace large portions of syllabi devoted to special solution methods, with problems of industrial magnitude and character.

scholarly journals Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method

2020 ◽  
Vol 226 ◽  
pp. 02007
Author(s):  
Galmandakh Chuluunbaatar ◽  
Alexander A. Gusev ◽  
Ochbadrakh Chuluunbaatar ◽  
Vladimir P. Gerdt ◽  
Sergue I. Vinitsky ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Hermite Polynomials ◽  
Analytical Form ◽  
Multivariate Interpolation ◽  
Partial Derivatives ◽  
Helmholtz Problem ◽  
Finite Element Schemes ◽  
Element Method

A new algorithm for constructing multivariate interpolation Hermite polynomials in analytical form in a multidimensional hypercube is presented. These polynomials are determined from a specially constructed set of values of the polynomials themselves and their partial derivatives with continuous derivatives up to a given order on the boundaries of the finite elements. The effciency of the finite element schemes, algor thms and programs is demonstrated by solving the Helmholtz problem for a cube.

Simulation of Axisymmetric Forming Processes, With Friction, Coupling Finite Elements and Boundary Elements

2006 ◽  
Author(s):  
Dominique Bigot ◽  
Hocine Kebir ◽  
Jean-Marc Roelandt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Finite Elements ◽  
Boundary Element ◽  
Symmetric Part ◽  
Forming Process ◽  
Optimal Shapes ◽  
Numerical Software ◽  
Element Method

Nowadays, the simulation of forming processes is rather well integrated in the industrial numerical codes. However, to take into account the possible modifications of the tool during cycle of working, we develop dedicated numerical software. This one more particularly will allow the identification of the fatigue criteria of the tool. With the view to conceiving the optimal shapes of tool allowing increasing their lifespan while ensuring a quality required of the part thus manufactured. This latter uses coupling with friction finite element method — for modelling the axi-symmetric part — and boundary element method — for modelling the tool. For the validation, we modeled forming process.

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