def ply_piece_area(self):
"""Get the area of a single ply piece that is on the free cone area,
i.e. between radii s2 and s3.
Returns
-------
area : float
The aforementioned area
"""
poly, pts_on_s2, pts_on_s3 = self._useful_polygon()
# Correct the area of the _useful_polygon to account for the arcs
s2_angle = abs(pts_on_s2[0].angle() - pts_on_s2[1].angle())
s3_angle = abs(pts_on_s3[0].angle() - pts_on_s3[1].angle())
area_s2 = circle_segment_area(self.cg.s2, s2_angle)
area_s3 = circle_segment_area(self.cg.s3, s3_angle)
return poly.area() - area_s2 + area_s3
def ply_piece_area(self):
"""Get the area of a single ply piece that is on the free cone area,
i.e. between radii s2 and s3.
Returns
-------
area : float
The aforementioned area
"""
poly, pts_on_s2, pts_on_s3 = self._useful_polygon()
# Correct the area of the _useful_polygon to account for the arcs
s2_angle = abs(pts_on_s2[0].angle() - pts_on_s2[1].angle())
s3_angle = abs(pts_on_s3[0].angle() - pts_on_s3[1].angle())
area_s2 = circle_segment_area(self.cg.s2, s2_angle)
area_s3 = circle_segment_area(self.cg.s3, s3_angle)
return poly.area() - area_s2 + area_s3
def effective_area(self, ply_piece=None, max_angle_dev=2.0):
"""Get the effective area of a single ply piece. This is the area on
useful section of the cone, where the deviation of the fiber angle
is less than a given maximum.
Parameters
----------
ply_piece : :class:`PlyPiece`, optional
Ply piece to get the effective area for. If not set, the base
piece is used.
max_angle_dev : float, optional
Maximum deviation from the nominal fiber angle to consider
the material 'effective'. In degrees.
Returns
-------
out : tuple
2-tuple, where ``out[0]`` is the effective surface area and
``out[1]`` is the corresponding polygon.
Notes
-----
Note that the polygon has straight edges, while the calculation of
the effective area takes into account that some edges of the effective
area may be arc sections.
"""
if ply_piece is None:
ply_piece = self.base_piece
poly, pts_on_s2, pts_on_s3 = self._useful_polygon(ply_piece)
# Construct lines through those corner points of the polygon,
# that are on s2/s3. They will be useful later
line_s2 = Line2D.from_points(*pts_on_s2)
line_s3 = Line2D.from_points(*pts_on_s3)
# Lines to cut away the non-effective area
cut_line_1 = Line2D.from_point_angle(Point2D(0., 0.),
ply_piece.phi_nom - np.radians(max_angle_dev))
cut_line_2 = Line2D.from_point_angle(Point2D(0., 0.),
ply_piece.phi_nom + np.pi + np.radians(max_angle_dev))
# Slice the polygon, with some corrections
for cut_line in (cut_line_1, cut_line_2):
outp = []
for p in poly.slice_line(cut_line).points():
# Polygon intersection can result in points that are not
# exactly on circles s2/s3, while they should be. Correct that.
if cut_line.distance_point(p) < TOL:
if line_s2.distance_point(p) < TOL:
p = cut_line.intersection_circle_near(self.cg.s2, p)
elif line_s3.distance_point(p) < TOL:
p = cut_line.intersection_circle_near(self.cg.s3, p)
outp.append(p)
poly = Polygon2D(outp)
# Calculate area
area = poly.area()
# Correct polygon area for arc sections s2/s3, if needed
pts_on_s2 = [p for p in poly.points() if abs(p.norm() - self.cg.s2) < TOL]
if len(pts_on_s2) >= 2:
angles = [p.angle() for p in pts_on_s2]
area -= circle_segment_area(self.cg.s2, max(angles) - min(angles))
pts_on_s3 = [p for p in poly.points() if abs(p.norm() - self.cg.s3) < TOL]
if len(pts_on_s3) >= 2:
angles = [p.angle() for p in pts_on_s3]
area += circle_segment_area(self.cg.s3, max(angles) - min(angles))
return area, poly
def effective_area(self, ply_piece=None, max_angle_dev=2.0):
"""Get the effective area of a single ply piece. This is the area on
useful section of the cone, where the deviation of the fiber angle
is less than a given maximum.
Parameters
----------
ply_piece : :class:`PlyPiece`, optional
Ply piece to get the effective area for. If not set, the base
piece is used.
max_angle_dev : float, optional
Maximum deviation from the nominal fiber angle to consider
the material 'effective'. In degrees.
Returns
-------
out : tuple
2-tuple, where ``out[0]`` is the effective surface area and
``out[1]`` is the corresponding polygon.
Notes
-----
Note that the polygon has straight edges, while the calculation of
the effective area takes into account that some edges of the effective
area may be arc sections.
"""
if ply_piece is None:
ply_piece = self.base_piece
poly, pts_on_s2, pts_on_s3 = self._useful_polygon(ply_piece)
# Construct lines through those corner points of the polygon,
# that are on s2/s3. They will be useful later
line_s2 = Line2D.from_points(*pts_on_s2)
line_s3 = Line2D.from_points(*pts_on_s3)
# Lines to cut away the non-effective area
cut_line_1 = Line2D.from_point_angle(
Point2D(0., 0.), ply_piece.phi_nom - np.radians(max_angle_dev))
cut_line_2 = Line2D.from_point_angle(
Point2D(0., 0.),
ply_piece.phi_nom + np.pi + np.radians(max_angle_dev))
# Slice the polygon, with some corrections
for cut_line in (cut_line_1, cut_line_2):
outp = []
for p in poly.slice_line(cut_line).points():
# Polygon intersection can result in points that are not
# exactly on circles s2/s3, while they should be. Correct that.
if cut_line.distance_point(p) < TOL:
if line_s2.distance_point(p) < TOL:
p = cut_line.intersection_circle_near(self.cg.s2, p)
elif line_s3.distance_point(p) < TOL:
p = cut_line.intersection_circle_near(self.cg.s3, p)
outp.append(p)
poly = Polygon2D(outp)
# Calculate area
area = poly.area()
# Correct polygon area for arc sections s2/s3, if needed
pts_on_s2 = [
p for p in poly.points() if abs(p.norm() - self.cg.s2) < TOL
]
if len(pts_on_s2) >= 2:
angles = [p.angle() for p in pts_on_s2]
area -= circle_segment_area(self.cg.s2, max(angles) - min(angles))
pts_on_s3 = [
p for p in poly.points() if abs(p.norm() - self.cg.s3) < TOL
]
if len(pts_on_s3) >= 2:
angles = [p.angle() for p in pts_on_s3]
area += circle_segment_area(self.cg.s3, max(angles) - min(angles))
return area, poly