From 9a5c2a76edd955e8098f28b650cfd6f7efbc9a25 Mon Sep 17 00:00:00 2001 From: Andrew Ning Date: Tue, 1 Oct 2024 17:14:41 -0600 Subject: [PATCH] slides --- atom.xml | 2 +- feed.xml | 2 +- me275/schedule/hw3sol/index.html | 183 +++++++++++++++++++++++++++ me275/schedule/hw5/index.html | 180 ++++++++++++++++++++++++++ me275/schedule/index.html | 12 +- me275/schedule/ravine.png | Bin 0 -> 73333 bytes me275/schedule/simpledata/index.html | 98 ++++++++++++++ 7 files changed, 469 insertions(+), 8 deletions(-) create mode 100644 me275/schedule/hw3sol/index.html create mode 100644 me275/schedule/hw5/index.html create mode 100644 me275/schedule/ravine.png create mode 100644 me275/schedule/simpledata/index.html diff --git a/atom.xml b/atom.xml index bd80d86..d65791c 100644 --- a/atom.xml +++ b/atom.xml @@ -4,7 +4,7 @@ FLOW Lab - 2024-09-27T14:57:09-06:00 + 2024-10-01T17:14:35-06:00 http://flow.byu.edu Andrew Ning diff --git a/feed.xml b/feed.xml index b8822b4..b7285ff 100644 --- a/feed.xml +++ b/feed.xml @@ -1 +1 @@ -Jekyll2024-09-27T14:57:09-06:00http://flow.byu.edu/feed.xmlFLOW LabFlight, Optimization, and Wind LaboratoryAndrew NingOptimization Book Available2021-10-15T00:00:00-06:002021-10-15T00:00:00-06:00http://flow.byu.edu/posts/opt-book]]>Andrew NingBEM Paper2021-07-30T00:00:00-06:002021-07-30T00:00:00-06:00http://flow.byu.edu/posts/bem-paper]]>Andrew NingEduardo Research Update2021-03-01T00:00:00-07:002021-03-01T00:00:00-07:00http://flow.byu.edu/posts/eduardo-latest]]>Eduardo AlvarezReformulated VPM2021-02-01T00:00:00-07:002021-02-01T00:00:00-07:00http://flow.byu.edu/posts/reformulated-vpm]]>Eduardo AlvarezOptimization Book Announcement2021-01-20T00:00:00-07:002021-01-20T00:00:00-07:00http://flow.byu.edu/posts/optimization-book]]>Andrew NingPJ Defense2020-09-30T00:00:00-06:002020-09-30T00:00:00-06:00http://flow.byu.edu/posts/pj-defense]]>Andrew NingVPM Paper2020-08-30T00:00:00-06:002020-08-30T00:00:00-06:00http://flow.byu.edu/posts/vpm-paper]]>Eduardo AlvarezAirborne Wind with Vortex Particle Method2020-08-16T00:00:00-06:002020-08-16T00:00:00-06:00http://flow.byu.edu/posts/wind-harvesting]]>Judd Mehr and Eduardo AlvarezEduardo’s Past Three Years2020-08-10T00:00:00-06:002020-08-10T00:00:00-06:00http://flow.byu.edu/posts/eduardo-three-years]]>Eduardo AlvarezFLOWUnsteady in Google Drive2020-08-02T00:00:00-06:002020-08-02T00:00:00-06:00http://flow.byu.edu/posts/google-drive-vpm]]>Eduardo Alvarez \ No newline at end of file +Jekyll2024-10-01T17:14:35-06:00http://flow.byu.edu/feed.xmlFLOW LabFlight, Optimization, and Wind LaboratoryAndrew NingOptimization Book Available2021-10-15T00:00:00-06:002021-10-15T00:00:00-06:00http://flow.byu.edu/posts/opt-book]]>Andrew NingBEM Paper2021-07-30T00:00:00-06:002021-07-30T00:00:00-06:00http://flow.byu.edu/posts/bem-paper]]>Andrew NingEduardo Research Update2021-03-01T00:00:00-07:002021-03-01T00:00:00-07:00http://flow.byu.edu/posts/eduardo-latest]]>Eduardo AlvarezReformulated VPM2021-02-01T00:00:00-07:002021-02-01T00:00:00-07:00http://flow.byu.edu/posts/reformulated-vpm]]>Eduardo AlvarezOptimization Book Announcement2021-01-20T00:00:00-07:002021-01-20T00:00:00-07:00http://flow.byu.edu/posts/optimization-book]]>Andrew NingPJ Defense2020-09-30T00:00:00-06:002020-09-30T00:00:00-06:00http://flow.byu.edu/posts/pj-defense]]>Andrew NingVPM Paper2020-08-30T00:00:00-06:002020-08-30T00:00:00-06:00http://flow.byu.edu/posts/vpm-paper]]>Eduardo AlvarezAirborne Wind with Vortex Particle Method2020-08-16T00:00:00-06:002020-08-16T00:00:00-06:00http://flow.byu.edu/posts/wind-harvesting]]>Judd Mehr and Eduardo AlvarezEduardo’s Past Three Years2020-08-10T00:00:00-06:002020-08-10T00:00:00-06:00http://flow.byu.edu/posts/eduardo-three-years]]>Eduardo AlvarezFLOWUnsteady in Google Drive2020-08-02T00:00:00-06:002020-08-02T00:00:00-06:00http://flow.byu.edu/posts/google-drive-vpm]]>Eduardo Alvarez \ No newline at end of file diff --git a/me275/schedule/hw3sol/index.html b/me275/schedule/hw3sol/index.html new file mode 100644 index 0000000..e094e6e --- /dev/null +++ b/me275/schedule/hw3sol/index.html @@ -0,0 +1,183 @@ + + + + + + + + + + + + + + HW Solution · ME 275 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +

HW 3 Solution

+ +
+ +
import numpy as np
+import math
+from scipy.optimize import root_scalar
+import matplotlib.pyplot as plt
+from scipy.integrate import cumulative_trapezoid, quad
+
+
+# --------- problem 1 --------------
+
+def shock(beta, theta, Mach):
+    num = Mach**2 * math.sin(beta)**2 - 1
+    den = Mach**2 * (1.4 + math.cos(2*beta)) + 2
+    return 2/math.tan(beta)*num/den - math.tan(theta)
+
+theta = 15*math.pi/180
+Mach = 2.0
+bmin = math.asin(1/Mach)
+bmax = 64*math.pi/180
+sol = root_scalar(shock, args=(theta, Mach), bracket=[bmin, bmax])
+print("----- problem 1 -------")
+print("shock angle (deg) =", sol.root*180/math.pi)
+
+
+# --------- problem 2 -------
+
+def newton(f, fp, x, tol):
+
+    deltax = 2*tol  # just some arbitrary value to make sure we enter the loop
+    iter = 0  # keep track of iterations
+    while abs(deltax) > tol:
+        deltax = f(x)/fp(x)
+        x -= deltax
+        iter += 1
+    return x, iter
+
+
+f = lambda x: x**3 - 3*x**2 + x - 1
+fp = lambda x: 3*x**2 - 6*x + 1
+tol = 1e-6
+xguess = 2.0
+sol, iter = newton(f, fp, xguess, tol)
+
+print("--- problem 2 ---")
+print("root =", sol)
+print("number of iterations", iter)
+
+
+# -------- problem 3 ------------
+# lift distribution function
+liftdist = lambda x: 4*np.sqrt(1 - 4*x**2)
+
+# trapezoidal integral
+npts = [10, 20, 40, 80, 160, 320]
+n = len(npts)
+I1 = np.zeros(n)
+for i in range(n):
+    x = np.linspace(-0.5, 0.5, npts[i])
+    I1[i] = np.trapz(liftdist(x), x)
+
+# Gaussian quadrature
+I2, err = quad(liftdist, -0.5, 0.5)
+
+plt.figure()
+plt.plot(npts, I1, "-o")
+plt.plot([10, 320], [I2, I2], "--")
+plt.xlabel("number of points")
+plt.ylabel("integral")
+plt.legend(["trapezoidal", "Gauss quad"])
+
+# -------- problem 4 ------------
+
+time, accel = np.loadtxt("accel.dat", unpack=True)
+vel = cumulative_trapezoid(accel, time, initial=0)
+
+plt.figure()
+plt.subplot(2, 1, 1)
+plt.plot(time, vel)
+plt.ylabel("velocity (m/s)")
+plt.subplot(2, 1, 2)
+plt.plot(time, accel)
+plt.xlabel("time (s)")
+plt.ylabel("acceleration (m/s^2)")
+plt.show()
+
+ +
+ + + diff --git a/me275/schedule/hw5/index.html b/me275/schedule/hw5/index.html new file mode 100644 index 0000000..db122df --- /dev/null +++ b/me275/schedule/hw5/index.html @@ -0,0 +1,180 @@ + + + + + + + + + + + + + + HW · ME 275 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +

HW 5

+ +

due 10/10/2024 before midnight via Learning Suite +25 possible points

+ +
+ +
    +
  1. +

    For the matrices and vectors defined below:

    + +\[A = \begin{bmatrix} + 1 & 2 & 3 \\ + 4 & 5 & 6 + \end{bmatrix} + \quad + b = + \begin{bmatrix} + 8\\ + 3\\ + 5 + \end{bmatrix} + \quad + C = \begin{bmatrix} + 1 & 2\\ + 3 & 4\\ + 5 & 6 + \end{bmatrix}\] + +

    Compute the following:

    + +\[a)\ A + C^T \quad b)\ 2 A \quad c)\ A b \quad d)\ b^T A^T \quad e)\ A A^T\] +
  2. +
  3. +

    Solve the following equations by writing the equation in matrix form and using a linear solver.

    + +\[4 = x_1 + 5 x_2 + 8 x_3 \\ + 6 x_1 + x_3 - 8 = 0\\ + 8x_2 - 3x_3 = 3 + 4 x_2 - 6 x_3\] +
  4. +
  5. +

    You are building a simple truss to suspend a load of 1000 lbs over a ravine. +

    + +

    Node A is the origin of our coordinate system, node B is at (1, 0), and the location of node C is something we are trying to design.

    + +

    a) Solve the problem with node C at (2, 1).

    + +

    b) Plot the stress in truss member AC with \(x_c\) varied from 1 (just over node B) to 3.

    +
  6. +
  7. +

    Given the following data points where \(y = f(x)\), we wish to determine a fit for the function \(f\) using linear least squares. Assume a quadratic function for \(f\), and plot the resulting data as a scatterplot and the curve fit as a solid line.

    + +
     x = np.array([-2.0000, -1.7895, -1.5789, -1.3684, -1.1579, -0.9474, -0.7368, -0.5263, -0.3158, -0.1053, 0.1053, 0.3158, 0.5263, 0.7368, 0.9474, 1.1579, 1.3684, 1.5789, 1.7895, 2.0000])
    + y = np.array([7.7859, 5.9142, 5.3145, 5.4135, 1.9367, 2.1692, 0.9295, 1.8957, -0.4215, 0.8553, 1.7963, 3.0314, 4.4279, 4.1884, 4.0957, 6.5956, 8.2930, 13.9876, 13.5700, 17.7481])
    +
    +
  8. +
+ + + +
+ + + diff --git a/me275/schedule/index.html b/me275/schedule/index.html index 0e9d53c..080d8e3 100644 --- a/me275/schedule/index.html +++ b/me275/schedule/index.html @@ -180,8 +180,8 @@

Schedule

Th Sep 26 Numerical Linear Algebra - 14.1-14.3 - HW 3 + 14.1-14.5 + HW 3, solution   @@ -191,13 +191,13 @@

Schedule

T Oct 1 - Solving Systems of Equations - 14.4-14.5 + Linear System Examples +   Quiz 4 Th Oct 3 - Linear Least Squares Regression + Linear Least Squares Ch 16 HW 4 @@ -209,7 +209,7 @@

Schedule

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+ + +
+ +
x = np.array([-2.0000, -1.7895, -1.5789, -1.3684, -1.1579, -0.9474, -0.7368, -0.5263, -0.3158, -0.1053, 0.1053, 0.3158, 0.5263, 0.7368, 0.9474, 1.1579, 1.3684, 1.5789, 1.7895, 2.0000])
+y = np.array([7.7859, 5.9142, 5.3145, 5.4135, 1.9367, 2.1692, 0.9295, 1.8957, -0.4215, 0.8553, 1.7963, 3.0314, 4.4279, 4.1884, 4.0957, 6.5956, 8.2930, 13.9876, 13.5700, 17.7481])
+
+ +
+ + +