scholarly journals Variants of the Finite Element Method for the Parabolic Heat Equation: Comparative Numerical Study

2020 ◽  
pp. 361-372
Author(s):  
Ahmed A. Hamada ◽  
Mahmoud Ayyad ◽  
Amr Guaily
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Equation ◽  
Numerical Study ◽  
The Finite Element Method ◽  
Element Method

Analysis of Aerodynamic Journal Bearings With Small Number of Herringbone Grooves by Finite Element Method

1994 ◽  
Vol 116 (4) ◽  
pp. 698-704 ◽  
Author(s):  
D. Bonneau ◽  
J. Absi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Load Capacity ◽  
Journal Bearings ◽  
The Finite Element Method ◽  
Bearing Number ◽  
Comparison Of The Results ◽  
Herringbone Grooves ◽  
Element Method

A numerical study of gas herringbone grooved journal bearings is presented for small number of grooves. The compressible Reynolds equation is solved by use of the Finite Element Method. The nonlinearity of the discretized equations is treated with the Newton-Raphson procedure. A comparison of the results for a smooth bearing with previously published results is made and the domain of validity of the Narrow Groove Theory is analyzed. Load capacity, attitude angle, and stiffness coefficients are given for various configurations: groove angle and thickness of grooves, bearing number, and that for both smooth and grooved member rotating.

An analytical approach to evaluate effective coefficients of 1–3 piezoelectric composites

2021 ◽  
Author(s):  
Sanjeev Kumar Singh ◽  
Saroja Kanta Panda
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Volume Fraction ◽  
Numerical Study ◽  
The Finite Element Method ◽  
Effective Coefficients ◽  
Square Packing ◽  
Packing Arrangement ◽  
Piezoelectric Fiber ◽  
Element Method

In this paper, a micromechanics method is developed to evaluate effective coefficients of piezoelectric fiber-reinforced composites. An exact solution is derived for effective elastic, piezoelectric and dielectric coefficients of such piezocomposites subjected to the applied load in the direction transverse to the fiber orientation. Simultaneously, based on finite element method, a numerical study is performed on a representative volume element of such piezo composite containing fiber in square packing arrangement. The finite element method provides a numerical solution to evaluate effective elastic, piezoelectric and dielectric coefficients for discrete volume fraction of fiber, the range being 0.1–0.6 for this study. The results are interpolated to understand the overall behavior of such piezocomposites. The results obtained from the micromechanics method and the finite element method are compared with the results obtained from other models based on strength of materials method given in the literature. It is observed that the method developed in this study provides better results for effective coefficients susceptible to fiber packing arrangements.

scholarly journals The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain

2018 ◽  
Vol 37 (4) ◽  
pp. 725-747 ◽  
Author(s):  
Jianlian Cheng ◽  
Kai Li ◽  
Zhuang Zhang ◽  
Yufeng Gu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Damping Ratio ◽  
Electrostatic Actuation ◽  
Compact Model ◽  
Squeeze Film ◽  
The Finite Element Method ◽  
Cantilever Structure ◽  
Element Method

Extensive modeling and simulation of the damping phenomenon, electrostatic actuation, and structural vibration analysis are performed. The governing partial differential equations of cantilever plate are obtained, and the resonant frequencies are calculated from the equilibrium equations. The damping forces of squeeze film are analyzed by obtaining the damping ratio and spring constant. Electrostatic actuation is applied to oscillate the cantilever to ensure that the displacement of the plate is above the thermal noise floor. Electrostatic actuating forces, displacement, and capacitance are calculated both numerically and analytically from the Poisson’s equations. Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Squeeze film effects are simulated by the finite element method. The accuracy of the compact model is studied by comparing its response to the numerical results calculated with the finite element method. The agreement is very good in a wide frequency band. The numerical study and the compact model are directly applicable in predicting the damping force and damping factors of squeeze film.

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