A calculational procedure of the Fermi–Dirac integral with an arbitrary real index by means of a numerical integration technique

1988 ◽  
Vol 63 (10) ◽  
pp. 5179-5181 ◽  
Author(s):  
Isao J. Ohsugi ◽  
Tsutomu Kojima ◽  
Isao Nishida
Keyword(s):  
Numerical Integration ◽  
Integration Technique ◽  
Calculational Procedure

Comparison of spectral methods for the evaluation of Stokes integral  

2021 ◽  
Author(s):  
Avadh Bihari Narayan ◽  
Ashutosh Tiwari ◽  
Govind Sharma ◽  
Balaji Devaraju ◽  
Onkar Dikshit
Keyword(s):  
Boundary Value Problems ◽  
Numerical Integration ◽  
Spectral Methods ◽  
Boundary Value ◽  
Fundamental Equation ◽  
Computation Time ◽  
Spherical Approximation ◽  
Integration Technique ◽  
Gravity Measurements ◽  
Stokes Integral

<p>The spherical approximation of the fundamental equation of geodesy defines the boundary value problems. Stokes’s integral provides the solution of boundary value problems that enables the computation of geoid from the properly reduced gravity measurements to the geoid. The stokes integral can be evaluated by brute-force numerical integration, spectral methods, and least-squares collocation. There is a trade-off between computation time and accuracy when we chose numerical integration technique or any spectral method. This research will compare time complexity and the accuracy of different spectral methods (1D-FFT, 2D-FFT, Multi-band FFT) and numerical integration technique for the region in the lower Himalaya, around Nainital, Uttarakhand, India. </p>

Efficient Updated-Lagrangian Simulations in Forming Processes

2015 ◽  
Vol 651-653 ◽  
pp. 1294-1300
Author(s):  
Diego Canales ◽  
Adrien Leygue ◽  
Francisco Chinesta ◽  
Elias Cueto ◽  
Eric Feulvarch ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Numerical Integration ◽  
General Purpose ◽  
Integration Technique ◽  
Numerical Examples ◽  
Nodal Integration ◽  
Out Of Plane ◽  
Material Forming ◽  
Updated Lagrangian ◽  
Stabilized Conforming Nodal Integration

A new efficient updated-Lagrangian strategy for numerical simulations of material forming processes is presented in this work. The basic ingredients are the in-plane-out-of-plane PGD-based decomposition and the use of a robust numerical integration technique (the Stabilized Conforming Nodal Integration). This strategy is of general purpose, although it is especially well suited for plateshape geometries. This paper is devoted to show the feasibility of the technique through some simple numerical examples.

A Method for the Calculation of Natural Frequencies of Orthotropic Axisymmetrically Loaded Shells of Revolution

1994 ◽  
Vol 116 (1) ◽  
pp. 16-25 ◽  
Author(s):  
A. Kayran ◽  
J. R. Vinson ◽  
E. Selcuk Ardic
Keyword(s):  
Numerical Integration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Shell Of Revolution ◽  
Initial Stresses ◽  
Integration Technique ◽  
Shells Of Revolution ◽  
Axisymmetric Loading

A methodology is presented for the calculation of the natural frequencies of orthotropic axisymmetrically loaded shells of revolution including the effect of transverse shear deformation. The fundamental system of equations governing the free vibration of the stress-free shells of revolution are modified such that the initial stresses due to the axisymmetric loading are incorporated into the analysis. The linear equations on the vibration about the deformed state are solved by using the transfer matrix method which makes use of the multisegment numerical integration technique. This method is commonly known as frequency trial method. The solution for the initial stresses due to axisymmetric loading is omitted; since the application of the transfer matrix method, making use of multisegment numerical integration technique for both linear and nonlinear equations are available in the literature. The method is verified by applying it to the solution of the natural frequencies of spinning disks, for which exact solutions exist in the literature, and a deep paraboloid for which approximate solutions exist. The governing equations for a shell of revolution are used to approximate circular disks by decreasing the curvature of the shell of revolution to very low values, and good agreement is seen between the results of the present method and the exact solution for spinning disks and the approximate solution for a deep paraboloid.

Study on the Dynamic Behavior of the Ball Passage Vibrations Associated with a Linear Rolling Bearing

2013 ◽  
Vol 325-326 ◽  
pp. 256-259
Author(s):  
Ting Chen ◽  
Qi Bai Huang ◽  
Shan De Li ◽  
Wei Guang Zheng
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Theoretical Result ◽  
Numerical Integration ◽  
Nonlinear Differential Equations ◽  
Rolling Bearing ◽  
Integration Technique ◽  
Nonlinear Dynamical ◽  
Proposed Model ◽  
Good Agreement

An analytical model to predict nonlinear dynamical responses of a linear rolling bearing due to ball passage vibrations has been developed. The implicit type numerical integration technique Runge-Kutta iterative method is used to solve the nonlinear differential equations. In order to verify the proposed model, experiments are carried out and good agreement between the theoretical result and that of measurement is achieved. It is helpful to use this model to design a satisfactory linear rolling bearing with comprehensively pleasant ball passage vibrations.

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