An Efficient Method for Calculating the Lightning Electromagnetic Field Over Perfectly Conducting Ground

In the implementation of the Cooray–Rubinstein formula, the calculation of a lightning electromagnetic field over perfectly conducting ground accounted for most of the computation time. Commonly, evaluating the ideal lightning electromagnetic field is based on the numerical integration method. In practice, only a sufficiently small discretization step is essential to get an accurate result, which leads to a relatively large number of calculations and results in a lengthy computation time. Besides, the programming is relatively complicated because the propagation of the lightning current along the channel must be considered. In order to increase the efficiency and simplify the programming, an improved method is proposed in this paper. In this method, the evaluation of the ideal lightning electromagnetic field is equated with a summation of analytical formulae and a simple integral operation, so it would be more efficient and easily programmed. The validation of the proposed method is demonstrated by some simulation examples.

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Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds

Journal of Vibration and Acoustics ◽

10.1115/1.4031617 ◽

2015 ◽

Vol 138 (1) ◽

Cited By ~ 18

Author(s):

Ye Ding ◽

Jinbo Niu ◽

LiMin Zhu ◽

Han Ding

Keyword(s):

Differential Equation ◽

Stability Analysis ◽

Numerical Integration ◽

Integration Method ◽

Transcendental Equation ◽

Spindle Speed ◽

Machining Parameters ◽

Numerical Integration Method ◽

Stability Diagrams ◽

Time Period

A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.

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The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1030-1032.223 ◽

2014 ◽

Vol 1030-1032 ◽

pp. 223-227

Author(s):

Lin Fan ◽

Song Rong Qian ◽

Teng Fei Ma

Keyword(s):

Differential Equation ◽

Integral Equation ◽

Numerical Integration ◽

Integration Method ◽

Equation Of Motion ◽

Numerical Integration Method ◽

Volume Integral ◽

Volume Integral Equation ◽

Method Of Molecular Dynamics ◽

Classic Theory

In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

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A New Method for Aggregate Proportion Design of Mixture

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.178-181.1250 ◽

2012 ◽

Vol 178-181 ◽

pp. 1250-1253

Author(s):

Yu Hua Li ◽

Kai Huang ◽

Ying Zhen Gao

Keyword(s):

Iterative Algorithm ◽

Accurate Result ◽

High Accuracy ◽

New Method ◽

Equation Method ◽

Normal Equation ◽

Improved Method ◽

Mixture Ratio ◽

Target Value ◽

Initial Target

When we make design of mixture ratio, we always use normal equation method (NEM), but the solution value of that method may doesn’t meet our demand. When we use the new method that proposed in this paper, we can solve the problem. The new method makes an improvement for NEM. By iterative algorithm, the new method uses the gradation data calculated by NEM as initial target value, canceling the relevant aggregate if the result of proportion is negative, and setting the gradation to the boundary value if the target value goes beyond limits. According to the adjusted object value, using NEM again, the new aggregate proportion can be solved. Then the new gradation of mixture will come into being the next target value. Finally, the accurate result will meet our need. The new improved method has good engineering applicability and high accuracy

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