Dr. Co Tran: New Applications
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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 19 Dec 2014 17:30:47 GMTFri, 19 Dec 2014 17:30:47 GMTNew applications published by Dr. Co Tranhttp://www.mapleprimes.com/images/mapleapps.gifDr. Co Tran: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=4820
FRACTURE PROPAGATION IN THE INTERNAL PRESSURIZED VESSEL .
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<p>** Abstract : -Calculating the maximum value Pmax that causes the fracture propagation while applying the internal static pressure . -Evaluating the time-limit for applying the continous / discrete form of internal dynamic pressure for the round metal vessel under conditions given by series expansion and curve -fitting method . ** Subjects: Fracture Mechanics , The stress intensity factor KI . This worksheet demonstrates Maple's capabilities in estimating the maximum pressure and the time-limit for applying static or dynamic pressure on the surface of a round metal vessel which has an internal semi-elliptical surface crack .</p><img src="/applications/images/app_image_blank_lg.jpg" alt="FRACTURE PROPAGATION IN THE INTERNAL PRESSURIZED VESSEL ." align="left"/><p>** Abstract : -Calculating the maximum value Pmax that causes the fracture propagation while applying the internal static pressure . -Evaluating the time-limit for applying the continous / discrete form of internal dynamic pressure for the round metal vessel under conditions given by series expansion and curve -fitting method . ** Subjects: Fracture Mechanics , The stress intensity factor KI . This worksheet demonstrates Maple's capabilities in estimating the maximum pressure and the time-limit for applying static or dynamic pressure on the surface of a round metal vessel which has an internal semi-elliptical surface crack .</p>35193Mon, 24 Dec 2012 05:00:00 ZDr. Co TranDr. Co TranFracture Propogation in the Internal Pressurized Vessel
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<p>** Abstract : -Calculating the maximum value Pmax that causes the fracture propagation while applying the internal static pressure . -Evaluating the time-limit for applying the continous / discrete form of internal dynamic pressure for the round metal vessel under conditions given by series expansion and curve -fitting method . ** Subjects: Fracture Mechanics , The stress intensity factor KI . This worksheet demonstrates Maple's capabilities in estimating the maximum pressure and the time-limit for applying static or dynamic pressure on the surface of a round metal vessel which has an internal semi-elliptical surface crack .</p><img src="/view.aspx?si=35194/thumb.jpg" alt="Fracture Propogation in the Internal Pressurized Vessel" align="left"/><p>** Abstract : -Calculating the maximum value Pmax that causes the fracture propagation while applying the internal static pressure . -Evaluating the time-limit for applying the continous / discrete form of internal dynamic pressure for the round metal vessel under conditions given by series expansion and curve -fitting method . ** Subjects: Fracture Mechanics , The stress intensity factor KI . This worksheet demonstrates Maple's capabilities in estimating the maximum pressure and the time-limit for applying static or dynamic pressure on the surface of a round metal vessel which has an internal semi-elliptical surface crack .</p>35194Sat, 20 Feb 2010 05:00:00 ZDr. Co TranDr. Co TranTHE SOLUTION STABILITY OF VAN DER POL’S EQUATION .
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<p>We consider the Van Der Pol differential equation and two topics that we will be in discussion are <br />
<br />
- Finding the steady state solution of this equation by averaging method .<br />
<br />
- Estimating the stability of solution obtained . <br />
This worksheet demonstrates Maple's capabilities in finding the graphical solution and dealing with the stability of the steady state solution of Van der Pol 's differential equation</p><img src="/view.aspx?si=33153/image.jpg" alt="THE SOLUTION STABILITY OF VAN DER POL’S EQUATION ." align="left"/><p>We consider the Van Der Pol differential equation and two topics that we will be in discussion are <br />
<br />
- Finding the steady state solution of this equation by averaging method .<br />
<br />
- Estimating the stability of solution obtained . <br />
This worksheet demonstrates Maple's capabilities in finding the graphical solution and dealing with the stability of the steady state solution of Van der Pol 's differential equation</p>33153Wed, 24 Jun 2009 04:00:00 ZDr. Co TranDr. Co TranTHE SOLUTION OF A VARIABLE BOUNDARY PROBLEM
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<img src="/view.aspx?si=5197/movement.jpg" alt="THE SOLUTION OF A VARIABLE BOUNDARY PROBLEM" align="left"/>5197Thu, 13 Sep 2007 00:00:00 ZDr. Co TranDr. Co TranThe Relaxation function problem of an orthotropic cylinder
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The worksheet presents some thoughts about the plane strain problem of the viscous orthotropic composite materials cylinder under internal and external pressure with respect to using the direct method. To compute the interior stress, from the elastic solution we use the correspondence principle and the inverse Laplace transform.
This worksheet demonstrates Maple's capabilities in researching the numerical and graphical solution of the relaxation function problem of an orthotropic cylinder.<img src="/view.aspx?si=5112/Relaxation_2.jpg" alt="The Relaxation function problem of an orthotropic cylinder" align="left"/>The worksheet presents some thoughts about the plane strain problem of the viscous orthotropic composite materials cylinder under internal and external pressure with respect to using the direct method. To compute the interior stress, from the elastic solution we use the correspondence principle and the inverse Laplace transform.
This worksheet demonstrates Maple's capabilities in researching the numerical and graphical solution of the relaxation function problem of an orthotropic cylinder.5112Tue, 24 Jul 2007 00:00:00 ZDr. Co TranDr. Co TranInvestigation of the Power Spectral Density of Duffing's Equation By Equivalent Linearization Method
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We consider the non-linear random vibration model demonstrated by the Duffing's differential equation. The stationary random process is f( t) which is satisfied < f(t) > = 0
with the spectral density function Sf ( w ) . To find the solution Sx ( w ) of (*) we use the equivalent linearization method .<img src="/view.aspx?si=4815/image.php.gif" alt="Investigation of the Power Spectral Density of Duffing's Equation By Equivalent Linearization Method" align="left"/>We consider the non-linear random vibration model demonstrated by the Duffing's differential equation. The stationary random process is f( t) which is satisfied < f(t) > = 0
with the spectral density function Sf ( w ) . To find the solution Sx ( w ) of (*) we use the equivalent linearization method .4815Tue, 05 Sep 2006 00:00:00 ZDr. Co TranDr. Co TranSolving the Viscous Composite Cylinder Problem by Sokolov's Method
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The paper presents some thoughts about the plane strain problem of the viscous orthotropic composite materials cylinder under internal and external pressure with respect to using the average approximating method . To compute the interior stress , from the elastic solution we use the Volterra’s principle and Sokolov’s method in the corresponding integral equation to find the viscous solution<img src="/view.aspx?si=1760/composite.jpg" alt="Solving the Viscous Composite Cylinder Problem by Sokolov's Method" align="left"/>The paper presents some thoughts about the plane strain problem of the viscous orthotropic composite materials cylinder under internal and external pressure with respect to using the average approximating method . To compute the interior stress , from the elastic solution we use the Volterra’s principle and Sokolov’s method in the corresponding integral equation to find the viscous solution1760Wed, 05 Jul 2006 00:00:00 ZDr. Co TranDr. Co TranFinite Difference Method and The Lame's Equation in Hereditary Solid Mechanics
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In this Maple Document, Lame's Equation is solved by the finite difference method.<img src="/view.aspx?si=1758/LAME_FDM940.gif" alt="Finite Difference Method and The Lame's Equation in Hereditary Solid Mechanics" align="left"/>In this Maple Document, Lame's Equation is solved by the finite difference method.1758Fri, 30 Jun 2006 00:00:00 ZDr. Co TranDr. Co TranThe Runge-Kutta Method for Solving Non-linear System of Differential Equations
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This application demonstrates Maple's capabilities in the design of a dynamic system and solving the non-linear SYSTEM of differential equations by Runge-Kutta method.<img src="/view.aspx?si=1751/Upload2.jpg" alt="The Runge-Kutta Method for Solving Non-linear System of Differential Equations" align="left"/>This application demonstrates Maple's capabilities in the design of a dynamic system and solving the non-linear SYSTEM of differential equations by Runge-Kutta method.1751Tue, 13 Jun 2006 00:00:00 ZDr. Co TranDr. Co TranThe Average Approximating Method on Functional Adjustment Quantity
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Solving the Volterra's integral equation II with applying the Neumann series and the average approximating method on functional adjustment quantity .
Viscoelasticity Mechanics , The Integral equation<img src="/view.aspx?si=1736/AvgApprox.jpg" alt="The Average Approximating Method on Functional Adjustment Quantity" align="left"/>Solving the Volterra's integral equation II with applying the Neumann series and the average approximating method on functional adjustment quantity .
Viscoelasticity Mechanics , The Integral equation1736Mon, 29 May 2006 00:00:00 ZDr. Co TranDr. Co TranNumerical and Graphical Solutions of Duffing Equation
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Duffing quation is solved by Runge-Kutta approximating method.
This worksheet demonstrates Maple's capabilities in the design of a dynamic system and finding the numerical solution of the Duffing equation.<img src="/view.aspx?si=1735/DuffingEqn.jpg" alt="Numerical and Graphical Solutions of Duffing Equation" align="left"/>Duffing quation is solved by Runge-Kutta approximating method.
This worksheet demonstrates Maple's capabilities in the design of a dynamic system and finding the numerical solution of the Duffing equation.1735Mon, 29 May 2006 00:00:00 ZDr. Co TranDr. Co Tran