Do we get the same result? Let's double-check: when substituting $r_1=2,r_2,=1,R_1=3,R_2=2$ in Ixgeneral, do we get the same result for Ix as obtained for the section initially considered?Īs expected, the general solution Ixgeneral reduces to the specific solution Ix when we substitute our original dimensions: vpa(subs(Ixgeneral, ,), 5) Now, let's substitute our symbolic parameters with the same values that we had in the first example. They can be set by using the assume and assumeAlso functions: syms x y r1 r2 R1 R2 In the Symbolic Math Toolbox, such restrictions are called assumptions on variables. For example, the system does not know if these variables are positive or negative, if $r_1 0$, $r_2>0$, $R_1>r_1$, and $R_2>r_2$. This is because the variables $r_1$, $r_2$, $R_1$, and $R_2$ can be any complex number, unless we explicitly restrict their values. Nevertheless, we need to add one more step: specify relationships between symbolic parameters. $y = \pm 2 \, \sqrt y^2\, \mathrm dy\, \mathrm dx.$$Īlthough the situation is more complicated now, we can still use the same strategy as above, using symbolic variables instead of numbers.The following ellipses define outer and inner contours of the section: The following picture shows the cross section of an elliptical tube. Basic Example: Cross Section of an Elliptical Tube
#Polar plot matlab r2013a code#
You can find the source code for these plots at the end of the article. We start with a basic case involving only numeric parameters, and then make the computations more general by introducing symbolic parameters.Īll plots used in this article have been created in the MuPAD Notebook app. In this article, we use capabilities of the Symbolic Math Toolbox to compute area moments for cross sections of elliptical tubes. For example, area moments of inertia play a critical role in stress, dynamic, and stability analysis of structures.
If you are interested in using MATLAB and the Symbolic Math Toolbox in teaching some basics in mechanical engineering, this might be of interest to you.Ĭomputing area moments of inertia is an important task in mechanics. In a Nutshell: What Is This Article About?
#Polar plot matlab r2013a how to#
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