Use your new matrices to calculate vector 2, with magnitude Z= sin(V x2 + y2) (a) Use the mesh plotting function to create a three-dimensional plot of z. Use the mesh- grid function to map x and y onto two new two-dimensional matrices called X and Y. Three-Dimensional Surface and Contour Plots 5.30 Create x and y vectors from 5 to +5 with a spacing of 0.5. In either MATLAB or FreeMat Make a contour plot called po3_contour.jpg, and a surface plot called po3_surface.jpg. In Freemat, a reasonable view angle can be achieved after plotting a surface using view(3). Don't worry about colormaps and interpolated shading. Use a text box to mark the yield point on your graph.ģ) Create an m-file called po3_surface.m and solve the following inside it: With Freemat you can only use the surf and contour functions. Once the material has been deformed past the yield point, the change in shape becomes permanent and is called plastic deformation. Before the yield point the material is elastic, returning to its original shape if the load is re moved- much like a rubber band. This corresponds to a significant change in the material behavior. (d) The point where the graph changes from a straight line with a steep slope to a flattened curve is called the yield stress or yield point. Connect the data points with a solid black line, and use circles to mark each data point (c) Add a title and appropriate axis labels. (b) Create an x-y plot with strain on the > axis and stress on the y-axis. The tested sample was a rod of diameter 0.505 in., so you'll need to find the cross-sectional area to use in your calculations. 1 = sample length 10 = original sample length (a) Use the provided data to calculate the stress and the corresponding strain for each data pair. (psi) F = applied force in lb A = sample cross-sectional area in in? E = strain in in /in. and ε = 1-10 o 10 where o = stress in lb/in. 149.) can be used to calculate the applied stress and the resulting strain with the following equations. These data Loa cell EN meter Specimen Figure P5.11 A tensile testing machine is used to measure stress and strain and to characterize the behavior of materials as they are deformed Moring cond An exam- ple set of data measured in one such test is shown in Table P5.11. The force (load) required to deform the material is measured, as is the resulting deformation. In the typical test, a specimen is stretched at a steady rate. 5.11 A tensile testing machine such as the one shown in Figure P5.11 is used to determine the behavior of materials as they are deformed. Save your final figure as po2 yieldPoint.jpg. 2) Create an m-file called po2_yieldPoint.m and solve the following inside it. 5.5 Adjust the plot created in Problem 5.4 so that the xaxis goes from -6 to +6. In general, markers are included only on plots of measured data, not for calculated values. Do not include markers on any of the graphs. Recall that the appropriate MATLAB® syntax for 2x is 2* x.) 5.4 Adjust the plot created in Problem 5.3 so that: 5.3 Plot the following functions on the same graph for x values from - to selecting spacing to create a smooth plot: 1 = sin(x) » = sin(2x) Ys = sin (3x) (Hint. Save your final figure as p01_sinewaves.jpg. 1) Create an m-file called p01_sinewaves.m and solve the following problem inside it. Don't forget to include your name, the date, etc. Each of your m-files should include appropriate comments to identify the problem and to describe your calculation process. Point MATLAB/Freemat to this folder and create a separate m-file for each problem below.
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