Mode III Fracture Mechanics Analysis With Fourier Series Method

1991 ◽  
Vol 44 (11S) ◽  
pp. S166-S170 ◽  
Author(s):  
F. W. M. Kwok ◽  
L. C. Kang ◽  
C. R. Steele
Keyword(s):  
Fourier Series ◽  
Fracture Mechanics ◽  
Multiple Cracks ◽  
Pure Mode ◽  
Polygonal Domain ◽  
Series Method ◽  
Mode Iii ◽  
Fourier Series Method ◽  
Out Of Plane ◽  
Good Agreement

A numerical scheme based on the Fourier series method is developed for the solution of Laplace’s equation on a polygonal domain. This scheme is applied to the solution of the pure mode III fracture mechanics problem. For the single edge cracked strip problem under out-of-plane loading, the value of the J-Integral evaluated from the Fourier solution was found to be in good agreement with classical solution. The real power of the scheme lies in its applicability to general polygonal shapes. This capability is illustrated by three sample problems that involve strips with a slanted crack, multiple cracks and branching cracks under mode III loading.

scholarly journals 1-D heat conduction in a fractal medium: A solution by the local fractional Fourier series method

2013 ◽  
Vol 17 (3) ◽  
pp. 953-956 ◽  
Author(s):  
Yuzhu Zhang ◽  
Aimin Yang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Series Method ◽  
Heat Transfer Mechanism ◽  
Basic Properties ◽  
Fractal Medium ◽  
Fourier Series Method

In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.

Development of the Low Cost Harmonic and Power Instrument by Using Fourier Series Method with Microcontroller

2014 ◽  
Vol 492 ◽  
pp. 519-525
Author(s):  
Napat Watjanatepin ◽  
Chaiyant Boonmee ◽  
Yutthana Kantaphayao
Keyword(s):  
Fourier Series ◽  
Power Factor ◽  
Measurement Errors ◽  
Single Phase ◽  
Low Cost ◽  
Electrical Power ◽  
Quality Measurement ◽  
Series Method ◽  
Electrical Parameters ◽  
Fourier Series Method

The objective of this paper is to present the application of microcontroller dsPIC30F6012A to measure the harmonics current and electrical power by using the Fourier series method to calculate the electrical parameters. This design is to develop the low cost harmonics instrument and to focus on working with the single phase AC system. The prototype was then developed to measure the harmonics current and power factor, and the result was compared with the standard instrument. The result is that most electrical parameters have the measurement errors of less than 4.0%. However, this idea could be developed so that it applies in the related work with the power quality measurement.

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