def shear_force(
self,
factor=None,
figsize=None,
verbosity=0,
scale=1,
offset=(0, 0),
show=True,
gridplot=False,
include_structure=True,
figure=None,
):
if include_structure:
self.plot_structure(
figsize, 1, scale=scale, offset=offset, gridplot=gridplot, figure=figure
)
con = len(self.system.element_map[1].shear_force)
if factor is None:
max_force = max(
map(
lambda el: np.max(np.abs(el.shear_force)),
self.system.element_map.values(),
)
)
factor = det_scaling_factor(max_force, self.max_val_structure)
color_counter = 0
for el in self.system.element_map.values():
if (
math.isclose(el.node_1.Ty, 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.node_2.Ty, 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.all_qp_load[0], 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.all_qp_load[1], 0, rel_tol=1e-5, abs_tol=1e-9)
):
# If True there is no bending moment and no shear, thus no shear force, so no need for plotting.
continue
iteration_factor = np.linspace(0, 1, con)
x = iteration_factor * el.l
eq = np.polyfit(x, el.bending_moment, 3)
x2, x = symbols("x² x")
section_function = str(round(-eq[0] * 3, 2) * x2 + round(-eq[1] * 2, 2) * x + round(-eq[2], 2))
axis_values = plot_values_shear_force(el, factor)
shear_1 = el.shear_force[0]
shear_2 = el.shear_force[-1]
self.plot_result(
axis_values, shear_1, shear_2, node_results=not bool(verbosity),
color=self.cs.color_list[color_counter], label=section_function
)
color_counter += 1
if color_counter > len(self.cs.color_list) - 1:
color_counter = 0
if show:
self.plot()
else:
return self.fig
def shear_force(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
if factor is None:
max_force = max(map(lambda el: np.max(np.abs(el.shear_force)), self.system.element_map.values()))
factor = det_scaling_factor(max_force, self.max_val_structure)
for el in self.system.element_map.values():
if math.isclose(el.node_1.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and \
math.isclose(el.node_2.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and el.q_load is None:
# If True there is no bending moment and no shear, thus no shear force, so no need for plotting.
continue
axis_values = plot_values_shear_force(el, factor)
shear_1 = el.shear_force[0]
shear_2 = el.shear_force[-1]
if verbosity == 0:
node_results = True
else:
node_results = False
self.plot_result(axis_values, shear_1, shear_2, node_results=node_results)
if show:
self.plot()
else:
return self.fig
def displacements(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, linear=False,
gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
if factor is None:
# needed to determine the scaling factor
max_displacement = max(map(
lambda el: max(abs(el.node_1.ux), abs(el.node_1.uz), el.max_deflection) if el.type == 'general' else 0,
self.system.element_map.values()))
factor = det_scaling_factor(max_displacement, self.max_val_structure)
for el in self.system.element_map.values():
axis_values = plot_values_deflection(el, factor, linear)
self.plot_result(axis_values, node_results=False)
if el.type == "general":
# index of the max deflection
index = np.argmax(np.abs(el.deflection))
if verbosity == 0:
x = (el.node_1.ux + el.node_2.ux) / 2
y = (-el.node_1.uz + -el.node_2.uz) / 2
if index != 0 or index != el.deflection.size:
self._add_element_values(axis_values[0], axis_values[1],
el.deflection[index] + (x ** 2 + y ** 2) ** 0.5, index, 3)
if show:
self.plot()
else:
return self.fig
def displacements(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, linear=False,
gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
if factor is None:
# needed to determine the scaling factor
max_displacement = max(map(
lambda el: max(abs(el.node_1.ux), abs(el.node_1.uz), el.max_deflection) if el.type == 'general' else 0,
self.system.element_map.values()))
factor = det_scaling_factor(max_displacement, self.max_val_structure)
for el in self.system.element_map.values():
axis_values = plot_values_deflection(el, factor, linear)
self.plot_result(axis_values, node_results=False)
if el.type == "general":
# index of the max deflection
index = np.argmax(np.abs(el.deflection))
if verbosity == 0:
x = (el.node_1.ux + el.node_2.ux) / 2
y = (-el.node_1.uz + -el.node_2.uz) / 2
if index != 0 or index != el.deflection.size:
self._add_element_values(axis_values[0], axis_values[1],
el.deflection[index] + (x ** 2 + y ** 2) ** 0.5, index, 3)
if show:
self.plot()
else:
return self.fig
def shear_force(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
if factor is None:
max_force = max(map(lambda el: np.max(np.abs(el.shear_force)), self.system.element_map.values()))
factor = det_scaling_factor(max_force, self.max_val_structure)
for el in self.system.element_map.values():
if math.isclose(el.node_1.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and \
math.isclose(el.node_2.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and el.q_load is None:
# If True there is no bending moment and no shear, thus no shear force, so no need for plotting.
continue
axis_values = plot_values_shear_force(el, factor)
shear_1 = el.shear_force[0]
shear_2 = el.shear_force[-1]
if verbosity == 0:
node_results = True
else:
node_results = False
self.plot_result(axis_values, shear_1, shear_2, node_results=node_results)
if show:
self.plot()
else:
return self.fig
def displacements(
self,
factor=None,
figsize=None,
verbosity=0,
scale=1,
offset=(0, 0),
show=True,
linear=False,
gridplot=False,
):
self.plot_structure(figsize,
1,
scale=scale,
offset=offset,
gridplot=gridplot)
if factor is None:
# needed to determine the scaling factor
max_displacement = max(
map(
lambda el: max(abs(el.node_1.ux), abs(el.node_1.uz), el.
max_deflection)
if el.type == "general" else 0,
self.system.element_map.values(),
))
factor = det_scaling_factor(max_displacement,
self.max_val_structure)
for el in self.system.element_map.values():
axis_values = plot_values_deflection(el, factor, linear)
self.plot_result(axis_values,
node_results=False,
fill_polygon=False)
if el.type == "general":
# index of the max deflection
x = np.linspace(el.vertex_1.x, el.vertex_2.x,
el.deflection.size)
y = np.linspace(el.vertex_1.y, el.vertex_2.y,
el.deflection.size)
xd, yd = plot_values_deflection(el, 1.0, linear)
deflection = ((xd - x)**2 + (yd - y)**2)**0.5
index = np.argmax(np.abs(deflection))
if verbosity == 0:
if index != 0 or index != el.deflection.size:
self._add_element_values(
axis_values[0],
axis_values[1],
deflection[index],
index,
3,
)
if show:
self.plot()
else:
return self.fig
def bending_moment(
self,
factor=None,
figsize=None,
verbosity=0,
scale=1,
offset=(0, 0),
show=True,
gridplot=False,
):
self.plot_structure(figsize,
1,
scale=scale,
offset=offset,
gridplot=gridplot)
con = len(self.system.element_map[1].bending_moment)
if factor is None:
# maximum moment determined by comparing the node's moments and the sagging moments.
max_moment = max(
map(
lambda el: max(el.bending_moment, )
if el.type == "general" else 0,
self.system.element_map.values(),
))
factor = det_scaling_factor(max_moment, self.max_val_structure)
# determine the axis values
for el in self.system.element_map.values():
if (math.isclose(el.node_1.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and
math.isclose(el.node_2.Ty, 0, rel_tol=1e-5, abs_tol=1e-9)
and not el.all_q_load):
# If True there is no bending moment, so no need for plotting.
continue
axis_values = plot_values_bending_moment(el, factor, con)
if verbosity == 0:
node_results = True
else:
node_results = False
self.plot_result(
axis_values,
abs(el.node_1.Ty),
abs(el.node_2.Ty),
node_results=node_results,
)
if el.all_q_load:
m_sag = min(el.bending_moment)
index = find_nearest(el.bending_moment, m_sag)[1]
offset = -self.max_val_structure * 0.05
if verbosity == 0:
x = axis_values[0][index] + np.sin(-el.angle) * offset
y = axis_values[1][index] + np.cos(-el.angle) * offset
self.one_fig.text(x, y, "%s" % round(m_sag, 1), fontsize=9)
if show:
self.plot()
else:
return self.fig
def bending_moment(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
con = len(self.system.element_map[1].bending_moment)
if factor is None:
# maximum moment determined by comparing the node's moments and the sagging moments.
max_moment = max(map(lambda el: max(abs(el.node_1.Ty),
abs((el.node_1.Ty - el.node_2.Ty) * 0.5 - 1 / 8
* el.all_q_load * el.l**2),) if el.type == 'general' else 0,
self.system.element_map.values()))
factor = det_scaling_factor(max_moment, self.max_val_structure)
# determine the axis values
for el in self.system.element_map.values():
if math.isclose(el.node_1.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and \
math.isclose(el.node_2.Ty, 0, rel_tol=1e-5, abs_tol=1e-9) and not el.all_q_load:
# If True there is no bending moment, so no need for plotting.
continue
axis_values = plot_values_bending_moment(el, factor, con)
if verbosity == 0:
node_results = True
else:
node_results = False
self.plot_result(axis_values, abs(el.node_1.Ty), abs(el.node_2.Ty), node_results=node_results)
if el.all_q_load:
m_sag = min(el.bending_moment)
index = find_nearest(el.bending_moment, m_sag)[1]
offset = -self.max_val_structure * 0.05
if verbosity == 0:
x = axis_values[0][index] + np.sin(-el.angle) * offset
y = axis_values[1][index] + np.cos(-el.angle) * offset
self.one_fig.text(x, y, "%s" % round(m_sag, 1),
fontsize=9)
if show:
self.plot()
else:
return self.fig
def axial_force(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
node_results = True if verbosity == 0 else False
if factor is None:
max_force = max(map(
lambda el: max(abs(el.N_1), abs(el.N_2)),
self.system.element_map.values()))
factor = det_scaling_factor(max_force, self.max_val_structure)
for el in self.system.element_map.values():
if math.isclose(el.N_1, 0, rel_tol=1e-5, abs_tol=1e-9):
continue
else:
axis_values = plot_values_axial_force(el, factor)
self.plot_result(axis_values, el.N_1, el.N_2, node_results=node_results)
point = (el.vertex_2 - el.vertex_1) / 2 + el.vertex_1
if el.N_1 < 0:
point.displace_polar(alpha=el.angle + 0.5 * np.pi, radius=0.5 * el.N_1 * factor, inverse_z_axis=True)
if verbosity == 0:
self.one_fig.text(point.x, point.y, "-", ha='center', va='center',
fontsize=20, color='b')
if el.N_1 > 0:
point.displace_polar(alpha=el.angle + 0.5 * np.pi, radius=0.5 * el.N_1 * factor, inverse_z_axis=True)
if verbosity == 0:
self.one_fig.text(point.x, point.y, "+", ha='center', va='center',
fontsize=14, color='b')
if show:
self.plot()
else:
return self.fig
def axial_force(self, factor=None, figsize=None, verbosity=0, scale=1, offset=(0, 0), show=True, gridplot=False):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot)
node_results = True if verbosity == 0 else False
if factor is None:
max_force = max(map(
lambda el: max(abs(el.N_1), abs(el.N_2)),
self.system.element_map.values()))
factor = det_scaling_factor(max_force, self.max_val_structure)
for el in self.system.element_map.values():
if math.isclose(el.N_1, 0, rel_tol=1e-5, abs_tol=1e-9):
continue
else:
axis_values = plot_values_axial_force(el, factor)
self.plot_result(axis_values, el.N_1, el.N_2, node_results=node_results)
point = (el.vertex_2 - el.vertex_1) / 2 + el.vertex_1
if el.N_1 < 0:
point.displace_polar(alpha=el.angle + 0.5 * np.pi, radius=0.5 * el.N_1 * factor, inverse_z_axis=True)
if verbosity == 0:
self.one_fig.text(point.x, point.y, "-", ha='center', va='center',
fontsize=20, color='b')
if el.N_1 > 0:
point.displace_polar(alpha=el.angle + 0.5 * np.pi, radius=0.5 * el.N_1 * factor, inverse_z_axis=True)
if verbosity == 0:
self.one_fig.text(point.x, point.y, "+", ha='center', va='center',
fontsize=14, color='b')
if show:
self.plot()
else:
return self.fig
def bending_moment(
self,
factor=None,
figsize=None,
verbosity=0,
scale=1,
offset=(0, 0),
show=True,
gridplot=False,
figure=None,
):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot, figure=figure)
con = len(self.system.element_map[1].bending_moment)
if factor is None:
# maximum moment determined by comparing the node's moments and the sagging moments.
max_moment = max(
map(
lambda el: max(
abs(el.node_1.Ty),
abs(el.node_2.Ty),
abs(((el.all_qp_load[0] + el.all_qp_load[1]) / 16) * el.l ** 2),
)
if el.type == "general"
else 0,
self.system.element_map.values(),
)
)
factor = det_scaling_factor(max_moment, self.max_val_structure)
color_counter = 0
# determine the axis values
for el in self.system.element_map.values():
if (
math.isclose(el.node_1.Ty, 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.node_2.Ty, 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.all_qp_load[0], 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.all_qp_load[1], 0, rel_tol=1e-5, abs_tol=1e-9)
):
# If True there is no bending moment, so no need for plotting.
continue
axis_values = plot_values_bending_moment(el, factor, con)
iteration_factor = np.linspace(0, 1, con)
x = iteration_factor * el.l
eq = np.polyfit(x, el.bending_moment, 3)
x3, x2, x = symbols("x³ x² x")
section_function = str(round(-eq[0], 2) * x3 + round(-eq[1], 2) * x2 + round(-eq[2], 2) * x +
round(-eq[3], 2))
if verbosity == 0:
node_results = True
else:
node_results = False
self.plot_result(
axis_values,
abs(el.node_1.Ty),
abs(el.node_2.Ty),
node_results=node_results,
color=self.cs.color_list[color_counter],
label=section_function,
)
color_counter += 1
if color_counter > len(self.cs.color_list) - 1:
color_counter = 0
if el.all_qp_load:
m_sag = min(el.bending_moment)
index = find_nearest(el.bending_moment, m_sag)[1]
offset = -self.max_val_structure * 0.05
if verbosity == 0:
x = axis_values[0][index] + np.sin(-el.angle) * offset
y = axis_values[1][index] + np.cos(-el.angle) * offset
self.one_fig.text(x, y, "%s" % round(m_sag, 1), fontsize=settings.size)
if show:
self.plot()
else:
return self.fig
def axial_force(
self,
factor=None,
figsize=None,
verbosity=0,
scale=1,
offset=(0, 0),
show=True,
gridplot=False,
figure=None,
):
self.plot_structure(figsize, 1, scale=scale, offset=offset, gridplot=gridplot, figure=figure)
con = len(self.system.element_map[1].axial_force)
if factor is None:
max_force = max(
map(
lambda el: max(
abs(el.N_1),
abs(el.N_2),
abs(((el.all_qn_load[0] + el.all_qn_load[1]) / 16) * el.l ** 2),
),
self.system.element_map.values(),
)
)
factor = det_scaling_factor(max_force, self.max_val_structure)
color_counter = 0
for el in self.system.element_map.values():
if (
math.isclose(el.N_1, 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.N_2, 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.all_qn_load[0], 0, rel_tol=1e-5, abs_tol=1e-9)
and math.isclose(el.all_qn_load[1], 0, rel_tol=1e-5, abs_tol=1e-9)
):
continue
else:
axis_values = plot_values_axial_force(el, factor, con)
color = 1 if el.N_1 < 0 else 0
self.plot_result(
axis_values,
el.N_1,
el.N_2,
node_results=not bool(verbosity),
color=self.cs.color_list[color_counter],
label=round(el.N_1, 2)
)
color_counter += 1
if color_counter > len(self.cs.color_list) - 1:
color_counter = 0
point = (el.vertex_2 - el.vertex_1) / 2 + el.vertex_1
if el.N_1 < 0:
point.displace_polar(
alpha=el.angle + 0.5 * np.pi,
radius=0.5 * el.N_1 * factor,
inverse_z_axis=True,
)
if verbosity == 0:
self.one_fig.text(
point.x,
point.y,
"-",
ha="center",
va="center",
fontsize=settings.size,
color=self.cs.axial_text,
)
if el.N_1 > 0:
point.displace_polar(
alpha=el.angle + 0.5 * np.pi,
radius=0.5 * el.N_1 * factor,
inverse_z_axis=True,
)
if verbosity == 0:
self.one_fig.text(
point.x,
point.y,
"+",
ha="center",
va="center",
fontsize=settings.size,
color=self.cs.axial_text,
)
if show:
self.plot()
else:
return self.fig
