From 9c35335a3074bdcf444ce6d2cc0b7c05ecf1284a Mon Sep 17 00:00:00 2001 From: Leahy Date: Thu, 14 Dec 2017 19:17:44 -0500 Subject: [PATCH] 1 --- README.md | 18 +++++++++++------- 1 file changed, 11 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index 87f3abc..fb77928 100644 --- a/README.md +++ b/README.md @@ -184,7 +184,7 @@ Using the bisect method, the tension in the membrane based on the conditions giv For a given pressure range of 0.001 to 0.01 MPa with 10 steps, determine the membrane tension using a root finding method at each pressure. Plot the results of pressure vs. maximum deflection and use a cubic best-fit line to determine the coefficient A, which is the best-fit constant for the line. ### Approach -Using the given pressure range, the tension was found at each different pressure value using the bisect method. The best fit line was found +Using the given pressure range, the tension is found at each different pressure value using the bisect method. From here, the deflection values at the calculated tensions and given pressures are found by calling the membrane_solution function from part C. The best fit line and coefficient are found using the built-in Matlab functions polyfit and polyval. These return a 4 x 1 matrix of coefficients, but since there is only one x term in the function (x^3), the first value in the matrix is determined to be the coefficient A. ```matlab clear @@ -217,12 +217,16 @@ Output - Based on 10 interior nodes: ## Part H ### Problem Statement +Show that the constant A is converging as the number of interior nodes is increased and display it in a table similar to the one seen in part F. + +### Approach +Running the code in Part G while increasing the number of nodes by 5 each time will yield the A constant. The relative error is found by calculating the difference between the error from the initial number of nodes to all of the subsequent node values. | number of nodes | Value of A | rel. error| | --- | --- | --- | -| 3 | | N/A | -| 20 | | | -| 25 | | | -| 30 | | | -| 35 | | | -| 40 | | | +| 3 | 0.3510 | N/A | +| 20 | 0.5622 | 37.57% | +| 25 | 0.6422 | 12.46% | +| 30 | 0.4932 | 30.21% | +| 35 | 0.5366 | 8.09% | +| 40 | 0.5339 | 0.51% |