Practical Applications of Finite Element Method

1978 ◽  
Vol 104 (1) ◽  
pp. 9-21
Author(s):  
Vera Dunder ◽  
Stephen Ridlon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Practical Applications ◽  
Element Method

Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

2011 ◽  
Vol 10 (2) ◽  
pp. 339-370 ◽  
Author(s):  
Yunqing Huang ◽  
Hengfeng Qin ◽  
Desheng Wang ◽  
Qiang Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Voronoi Tessellation ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Adaptive Procedure ◽  
Seamless Integration ◽  
Practical Applications ◽  
Element Method

AbstractWe present a novel adaptive finite element method (AFEM) for elliptic equations which is based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation (CVDT) are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes. Working with finite element solutions on such high quality triangulations, superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained. Through a seamless integration of these techniques, a convergent adaptive procedure is developed. As demonstrated by the numerical examples, the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

Impacting a Clamped-Free Beam to Experimentally and Numerically Determine Higher Resonant Frequencies of Vibration

2016 ◽  
Author(s):  
Elvin B. Shields
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Experimental Method ◽  
Experimental Methods ◽  
Film Material ◽  
Resonant Frequencies ◽  
Practical Applications ◽  
Condenser Microphone ◽  
Normal Means ◽  
Element Method

Clamped-free (cantilever) beams have practical applications. For example, it is not possible to use normal means to determine the modulus of elasticity for thin films. However, the film material can be deposited onto the beam substrate by sputtering or by applying the additive manufacturing technique and thereby change the beam’s stiffness as suggested by Dias da Silva et al [1]. The stiffness change causes a shift in the natural frequencies of the vibration of the beam and this shift can be used to determine the material properties of the film. This study provides four methods of analysis: 1) formula calculation, which is used as the benchmark, 2) finite element method, 3) experimental method with accelerometer, and 4) experimental method with condenser microphone. Theoretical results are used as benchmarks and compared with the finite element method (FEM) and two experimental methods (accelerometer and condenser microphone). The challenge is to obtain results with the necessary accuracy (significant digits) at higher resonant frequencies of vibration. The two experimental methods were evaluated and the experimental method with condenser microphone showed the most promise for future work. Very little was found in the literature regarding the use of a condenser microphone to measure resonant frequencies.

scholarly journals Potential of Room Acoustic Solver with Plane-Wave Enriched Finite Element Method

2020 ◽  
Vol 10 (6) ◽  
pp. 1969 ◽  
Author(s):  
Takeshi Okuzono ◽  
M Shadi Mohamed ◽  
Kimihiro Sakagami
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Degrees Of Freedom ◽  
Plane Waves ◽  
Complex Impedance ◽  
Helmholtz Resonator ◽  
Room Acoustics ◽  
Practical Applications ◽  
Element Method

Predicting room acoustics using wave-based numerical methods has attracted great attention in recent years. Nevertheless, wave-based predictions are generally computationally expensive for room acoustics simulations because of the large dimensions of architectural spaces, the wide audible frequency ranges, the complex boundary conditions, and inherent error properties of numerical methods. Therefore, development of an efficient wave-based room acoustic solver with smaller computational resources is extremely important for practical applications. This paper describes a preliminary study aimed at that development. We discuss the potential of the Partition of Unity Finite Element Method (PUFEM) as a room acoustic solver through the examination with 2D real-scale room acoustic problems. Low-order finite elements enriched by plane waves propagating in various directions are used herein. We examine the PUFEM performance against a standard FEM via two-room acoustic problems in a single room and a coupled room, respectively, including frequency-dependent complex impedance boundaries of Helmholtz resonator type sound absorbers and porous sound absorbers. Results demonstrated that the PUFEM can predict wideband frequency responses accurately under a single coarse mesh with much fewer degrees of freedom than the standard FEM. The reduction reaches O ( 10 − 2 ) at least, suggesting great potential of PUFEM for use as an efficient room acoustic solver.

On the Application of Finite Element Method (FEM) to the Slope Stability Analyses

2011 ◽  
Vol 66-68 ◽  
pp. 1913-1916
Author(s):  
Guo Lin Xu ◽  
Hao Huang ◽  
Ya Shuang Bai ◽  
Wen Sheng Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slope Stability ◽  
Poisson Ratio ◽  
Strength Reduction ◽  
The Finite Element Method ◽  
Practical Applications ◽  
Stability Analyses ◽  
Gravity Increase Method ◽  
Element Method

The finite element method (FEM) is widely adopted in the geotechnical engineering, but there exist some problems in practical applications, such as the lack of unified standard to determine parameters and the limitation of the calculation method. This article determines the reasonable value of Poisson ratio, by comparing different Poisson ratios selected in the strength reduction of FEM calculations, and improves the gravity increase method in order to enhance its accuracy in the gentle slope stability analyses.

scholarly journals NUMERICAL STABILITY AND ACCURACY OF THE SCALED BOUNDARY FINITE ELEMENT METHOD IN ENGINEERING APPLICATIONS

2015 ◽  
Vol 57 (2) ◽  
pp. 114-137 ◽  
Author(s):  
MIAO LI ◽  
YONG ZHANG ◽  
HONG ZHANG ◽  
HONG GUAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Stability ◽  
Solid Mechanics ◽  
Computational Method ◽  
Theoretical Development ◽  
Practical Applications ◽  
Stability And Accuracy ◽  
Scaled Boundary Finite Element ◽  
Element Method

The scaled boundary finite element method (SBFEM) is a semi-analytical computational method initially developed in the 1990s. It has been widely applied in the fields of solid mechanics, oceanic, geotechnical, hydraulic, electromagnetic and acoustic engineering problems. Most of the published work on SBFEM has focused on its theoretical development and practical applications, but, so far, no explicit discussion on the numerical stability and accuracy of its solution has been systematically documented. However, for a reliable engineering application, the inherent numerical problems associated with SBFEM solution procedures require thorough analysis in terms of its causes and the corresponding remedies. This study investigates the numerical performance of SBFEM with respect to matrix manipulation techniques and their properties. Some illustrative examples are given to identify reasons for possible numerical difficulties, and corresponding solution schemes are proposed to overcome these problems.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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