add computation of section properties

Author: PetrKryslUCSD

examples/i_beam.py

@@ -0,0 +1,35 @@
+"""
+
+"""
+
+from numpy import array, dot
+from numpy.linalg import cross
+from context import pystran
+from pystran import model
+from pystran import section
+
+H = 0.3
+B = 0.15
+tf = 0.01
+tw = 0.005
+# p = section.i_beam_points(H, B, tf, tw)
+# print(section.area(p))
+# print(section.centroid(p))
+# p = p - section.centroid(p)
+# print(section.centroid(p))
+# print(section.inertias(p))
+
+Iy = (B / 12) * H**3 - ((B - tw) / 12) * (H - 2 * tf) ** 3
+print(Iy)
+Iz = (
+    H * B**3 / 12
+    - 2 * ((B - tw) / 2) ** 3 * (H - 2 * tf) / 12
+    - 2 * ((B - tw) / 2) * (H - 2 * tf) * ((B - tw) / 4 + tw / 2) ** 2
+)
+print(Iz)
+# # Iy = (a3 h / 12) + (b3 / 12) (H - h)
+
+A, Ix, Iy, Iz, J = section.i_beam(H, B, tf, tw)
+print(A, Ix, Iy, Iz, J)
+
+print((2 * B * tf**3 + (H - 2 * tf) * tw**3) / 3)

pystran/section.py

@@ -5,6 +5,9 @@
 second moment of area, and also orientation of the cross section profile.
 """
 
+from math import pi
+import numpy
+
 
 def truss_section(name, E=0.0, A=0.0, rho=0.0):
     """
@@ -46,7 +49,7 @@ def beam_3d_section(
     Iz=0.0,
     J=0.0,
     rho=0.0,
-    xz_vector=[0, 0, 1],
+    xz_vector=(0, 0, 1),
 ):
     """
     Define 3d beam section.
@@ -71,3 +74,49 @@ def beam_3d_section(
     s["J"] = J
     s["xz_vector"] = xz_vector
     return s
+
+
+def close_points(points):
+    """
+    If the input points do not form a closed polygon, closes the polygon
+    and returns the result.
+
+    Parameters
+    ----------
+    points : array
+        An array of (x, y) coordinates of shape (N, 2).
+    """
+    p = numpy.asarray(points)
+    if (p[0] == p[-1]).all():
+        return p
+    return numpy.append(p, [p[0]], axis=0)
+
+
+def hollow_circle(innerradius, outerradius):
+    """
+    Returns the area, moments of inertia and torsion constant for a hollow circle (tube).
+    """
+    Rext = outerradius
+    Rint = innerradius
+    A = pi * (Rext ^ 2 - Rint ^ 2)
+    Iy = pi / 4 * (Rext ^ 4 - Rint ^ 4)
+    Iz = pi / 4 * (Rext ^ 4 - Rint ^ 4)
+    Ix = Iy + Iz
+    J = pi / 2 * (Rext ^ 4 - Rint ^ 4)
+    return A, Ix, Iy, Iz, J
+
+
+def i_beam(H, B, tf, tw):
+    """
+    Returns the area, moments of inertia and torsion constant for an I-beam.
+    """
+    A = B * H - (B - tw) * (H - 2 * tf)
+    Iy = (B / 12) * H**3 - ((B - tw) / 12) * (H - 2 * tf) ** 3
+    Iz = (
+        H * B**3 / 12
+        - 2 * ((B - tw) / 2) ** 3 * (H - 2 * tf) / 12
+        - 2 * ((B - tw) / 2) * (H - 2 * tf) * ((B - tw) / 4 + tw / 2) ** 2
+    )
+    Ix = Iy + Iz
+    J = (2 * B * tf**3 + (H - 2 * tf) * tw**3) / 3
+    return A, Ix, Iy, Iz, J