Multi-domain multi-scale problems in high frequency finite element methods

Author(s):  
Istvan Bardi ◽  
Kezhong Zhao ◽  
Rickard Petersson ◽  
John Silvestro ◽  
Nancy Lambert
2019 ◽  
Vol 17 (09) ◽  
pp. 1950060
Author(s):  
Tengfei Dai ◽  
Xia Jin ◽  
Huaze Yang ◽  
Tianran Lin ◽  
Yuantong Gu

Modeling and simulation of the acoustic response in enclosed cavities of a diesel engine are of great significance for optimal design of an engine to achieve a better acoustic performance. Nevertheless, the use of the traditional finite element method (FEM) for the mid to high frequency acoustic prediction is limited by the well-known numerical dispersion errors and the tedious preprocessing of the model. Smoothed finite element methods (SFEMs) proposed originally for solid mechanics have been employed for the modeling of acoustic problems in the low to medium frequency ranges whilst acoustic modeling in the mid to high frequency range remains untouched. This paper comprehensively investigates into the performance of SFEMs in modeling and simulation of mid to high frequency acoustic problems. It is shown that the mass-redistributed edge-based smoothed finite element method (MR-ES-FEM) can yield an excellent prediction result in the mid to high frequency range in terms of accuracy, efficiency and robustness. The MR-ES-FEM is also used to simulate sound propagation in a cylinder head chamber of a four-cylinder diesel engine to prove its effectiveness. The findings presented in this paper offer an in-depth insight for engineers to select suitable numerical methods for solving mid to high frequency acoustic problems in the design of diesel engines.


Author(s):  
Jia Geng ◽  
Xingwu Zhang ◽  
Xuefeng Chen ◽  
Xiaofeng Xue

For the dynamic analysis of thin plate bending problems, the Finite Element Methods (FEMs) are the most commonly used numerical techniques in engineering. However, due to the deficiency of low computing efficiency and accuracy, the FEMs can’t be directly used to effectively evaluate dynamic analysis of thin plate with high modal density within low-high frequency domain. In order to solve this problem, the Wavelet Finite Element Methods (WFEMs) has been introduced to solve the problem by improving the computing efficiency and accuracy in this paper. Due to the properties of multi-resolution, the WFEMs own excellently high computing efficiency and accuracy for structure analysis. Furthermore, for the destination of predicting dynamic response of thin plate within high frequency domain, this paper introduces the Multi-wavelet element method based on c1 type wavelet thin plate element and a new assembly procedure to significantly promote the calculating efficiency and accuracy which aim at breaking up the limitation of frequency domain when using the existing WFEMs and traditional FEMs. Besides, the numerical studies are applied to certify the validity of the method by predicting state response of thin plate within 0∼1000Hz based on a special numerical example with high modal density. According to the literature, the frequency domain between 0 to 1000Hz contains the low-high frequency domain aiming at the numerical example. The numerical results show excellent agreement with the reference solutions captured by FEM and analytical expressions respectively. Among these, it is noteworthy that the relative errors between the analytical solutions and numerical solution are less than 0.4% when the dynamic response involved with 1000 modes.


2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.


1983 ◽  
Author(s):  
W. HABASHI ◽  
M. HAFEZ ◽  
P. KOTIUGA

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