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add structure plate

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This commit is contained in:
Daniel Weschke
2026-01-11 18:24:42 +01:00
parent 1f9ebe926f
commit 710506b4aa
2 changed files with 200 additions and 37 deletions
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200
src/fvr/structure.py
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@@ -1,18 +1,23 @@
"""Structure :py:class:`beam` and :py:class:`tube` objects.
"""Structure :py:class:`Beam` and :py:class:`Tube` objects.
"""
import numpy as np
class beam:
"""Euler-Bernoulli beam.
"""
def __init__(self, E, I, A, L, rho):
class Beam:
r"""Euler-Bernoulli beam.
"""
def __init__(self, E: float, I: float, A: float, L: float, rho: float):
r"""
Args:
E: Elastic modulus / Young's modulus
I: Second moment of area of the beam's cross-section
A: Cross-section
L: Length
rho: Density
.. math::
I = \frac{h^3}{12}
"""
self.E = E
self.I = I
@@ -21,20 +26,20 @@ class beam:
self.rho = rho
@property
def V(self):
def V(self) -> float:
return self.A * self.L
@property
def mu(self):
def mu(self) -> float:
"""Mass per unit length (or the product of density and cross-section)"""
return self.rho * self.A
@property
def m(self):
def m(self) -> float:
return self.mu * self.L
# return self.rho * self.V
def eigenfrequency(self, n:int, support : str = 'fixed-free') -> float:
def eigenfrequency(self, n: int, support: str = 'fixed-free') -> float:
r"""Natural frequencies of the beam.
Args:
@@ -104,19 +109,18 @@ class beam:
f_n = \frac{a_n^2}{2\pi}\sqrt{\frac{E\,I}{\mu}}
"""
a_nLopi = [0.596864, 1.49418, 2.50025, 3.49999]
a_n = a_nLopi[n-1]*np.pi/self.L if n < len(a_nLopi) else 0
return a_n**2*np.sqrt(self.E*self.I/self.mu)/(2*np.pi)
a2_n = [0.596864, 1.49418, 2.50025, 3.49999] # a_n*L/pi
a_n = a2_n[n - 1] * np.pi / self.L if n < len(a2_n) else 0
return a_n**2 * np.sqrt(self.E * self.I / self.mu) / (2 * np.pi)
class tube:
class TubeBuckling:
r"""Long thin circular tube uniformly loaded with external pressure.
Elemental ring of unit width (h)
IMPORTANT: Can be used as long as the corresponding compressive stress does
not exeed the proportional limit of the material.
:math:`I = \frac{h^3}{12}`
Important:
Can be used as long as the corresponding compressive stress does not exeed
the proportional limit of the material.
References:
- Timoshenko, Stephen P., and James M. Gere. 1961. Theory of Elastic
@@ -124,7 +128,9 @@ class tube:
"""
def __init__(self, E, nu, r, *, h=None, q=None, s=None):
def __init__(
self, E: float, nu: float, r: float, *, h: float | None = None,
q: float | None = None, s: float | None = None):
r"""
Args:
E: Young's modulus
@@ -137,11 +143,14 @@ class tube:
self.E = E
self.nu = nu
self.r = r
if (h or q or s):
pass
self.h = h
self.s = s
self.q = q
def buckling_force(self):
def force(self) -> float:
r"""Critical buckling value of the compressive force.
A long circular tube uniformly compressed by external pressure.
@@ -155,9 +164,11 @@ class tube:
Stability. 2nd ed. New York: McGraw-Hill Book. p. 289.
"""
if self.h is None:
raise ValueError("h is not defined.")
return (self.E * self.h**3) / (4 * (1 - self.nu**2) * self.r**2)
def buckling_pressure(self):
def pressure(self) -> float:
r"""Critical buckling value of the compressive pressure.
A long circular tube uniformly compressed by external pressure.
@@ -175,9 +186,11 @@ class tube:
Stability. 2nd ed. New York: McGraw-Hill Book. p. 289.
"""
if self.h is None:
raise ValueError("h is not defined.")
return self.E / (4 * (1 - self.nu**2)) * (self.h / self.r)**3
def buckling_stress(self):
def stress(self) -> float:
r"""Critical buckling stress of a long thin circular tube uniformly
compressed by pressure.
@@ -194,36 +207,153 @@ class tube:
Stability. 2nd ed. New York: McGraw-Hill Book. p. 293.
"""
if self.h is None:
raise ValueError("h is not defined.")
return self.E / (1 - self.nu**2) * (self.h / (2 * self.r))**2
def buckling_thickness(self) -> float|None:
def thickness(self) -> float | None:
r"""Critical buckling thickness of a long thin circular tube uniformly
compressed by external pressure.
Returns:
- Thickness regarding the internal stress, if stress is given
.. math::
h_{\text{cr,}\sigma} = \sqrt{\sigma_\text{cr} \frac{1 - \nu^2}{E}} {2r}
- Thickness regarding the external pressure, if pressure is given
- Otherwise given thickness
- Or None
See also:
:py:meth:`buckling_thickness_pressure` and
:py:meth:`buckling_thickness_stress`
"""
if self.s is not None:
return self.thickness_stress()
if self.q is not None:
return self.thickness_pressure()
if self.h is not None:
return self.h
return None
def thickness_pressure(self) -> float:
r"""Critical buckling thickness of a long thin circular tube uniformly
compressed by external pressure.
Thickness regarding the external pressure
.. math::
h_\text{cr,q} = \left(q_\text{cr} \, 4 \frac{1 - \nu^2}{E}\right)^\frac{1}{3} {r}
- Otherwise given thickness or None
h_\text{cr,q} = \left(q_\text{cr} \, 4
\frac{1 - \nu^2}{E}\right)^\frac{1}{3} {r}
References:
- Timoshenko, Stephen P., and James M. Gere. 1961. Theory of Elastic
Stability. 2nd ed. New York: McGraw-Hill Book. p. 293.
"""
if self.scr is not None:
if self.q is None:
raise ValueError("q is not defined.")
return np.power(self.q * 4 * (1 - self.nu**2) / self.E, 1 / 3) * self.r
def thickness_stress(self) -> float:
r"""Critical buckling thickness of a long thin circular tube uniformly
compressed by external pressure.
Thickness regarding the internal stress
.. math::
h_{\text{cr,}\sigma} = \sqrt{\sigma_\text{cr} \frac{1 - \nu^2}{E}} {2r}
References:
- Timoshenko, Stephen P., and James M. Gere. 1961. Theory of Elastic
Stability. 2nd ed. New York: McGraw-Hill Book. p. 293.
"""
if self.s is None:
raise ValueError("s is not defined.")
return np.sqrt(self.s * (1 - self.nu**2) / self.E) * (2 * self.r)
if self.qcr is not None:
return np.power(self.q * 4 * (1 - self.nu**2) / self.E, 1/3) * self.r
if self.h is not None:
return self.h
class Plate:
r"""Thin circular plate uniformly loaded with external pressure.
Important:
Can be used as long as the corresponding stress does not exeed the
proportional limit of the material.
References:
- Timoshenko, Stephen P., and S. Woinowsky-Krieger. 1959. Theory of Plates
and Shells. 2nd ed. New York: McGraw-Hill Book.
"""
def __init__(self, E: float, nu: float, ra: float, h: float):
"""
Args:
E: Elastic modulus / Young's modulus
nu: Poisson's ratio
ra: radius
h: thickness
"""
self.E = E
self.nu = nu
self.ra = ra
self.h = h
@property
def D(self) -> float:
r"""Flexural rigidity of the plate.
.. math::
D = \frac{E\,h^3}{12(1-\nu^2)}
"""
return self.E * self.h**3 / (12 * (1 - self.nu**2))
def deflection(self, q, support: str = 'clamped') -> float | None:
r"""Central deflection of a clamped supported circular plate.
Args:
q: external pressure
support: clamped, simple
See also:
:py:meth:`deflection_clamped` and :py:meth:`deflection_simple`
"""
if support == 'clamped':
return self.deflection_clamped(q)
elif support == 'simple':
return self.deflection_simple(q)
return None
def deflection_clamped(self, q) -> float:
r"""Central deflection of a clamped supported circular plate.
Args:
q: external pressure
.. math::
w_\text{max} = \frac{q \, r_\text{a}^4}{64D}
References:
- Timoshenko, Stephen P., and S. Woinowsky-Krieger. 1959. Theory of Plates
and Shells. 2nd ed. New York: McGraw-Hill Book. p. 55.
"""
return q * self.ra**4 / (64 * self.D)
def deflection_simple(self, q) -> float:
r"""Central deflection of a simple/pinned supported circular plate.
Args:
q: external pressure
.. math::
w_\text{max} = \frac{q \, r_\text{a}^4}{64D} \frac{5+\nu}{1+\nu}
References:
- Timoshenko, Stephen P., and S. Woinowsky-Krieger. 1959. Theory of Plates
and Shells. 2nd ed. New York: McGraw-Hill Book. p. 57.
"""
return q * self.ra**4 / (64 * self.D) * (5 + self.nu) / (1 + self.nu)

35
tests/test_structure.py
View File

@@ -6,15 +6,48 @@ import fvr.structure
class TestStructureBeam(unittest.TestCase):
def setUp(self):
self.obj = fvr.structure.beam(1, 2, 3, 4, 5)
self.obj = fvr.structure.Beam(1, 2, 3, 4, 5)
def test_volume(self):
self.assertEqual(self.obj.V, 12, 'incorrect volume after creation')
def test_volume_a(self):
self.obj.A = 6
self.assertEqual(self.obj.V, 24, 'incorrect volume after changing A')
def test_volume_l(self):
self.obj.L = 7
self.assertEqual(self.obj.V, 21, 'incorrect volume after changing L')
def test_mu(self):
self.assertEqual(self.obj.mu, 15, 'incorrect specific mass after creation')
def test_m(self):
self.assertEqual(self.obj.m, 60, 'incorrect mass after creation')
def test_eigenfrequency(self):
self.assertEqual(
self.obj.eigenfrequency(1), 0.012770856732837836,
'incorrect eigen-frequency after creation')
class TestStructureTubeBuckling(unittest.TestCase):
def setUp(self):
self.obj = fvr.structure.TubeBuckling(1, 0.2, 3, h=4)
def test_force(self):
self.assertEqual(
self.obj.force(), 1.8518518518518516,
'incorrect buckling force after creation')
def test_pressure(self):
self.assertEqual(
self.obj.pressure(), 0.6172839506172838,
'incorrect buckling force after creation')
def test_stress(self):
self.assertEqual(
self.obj.stress(), 0.46296296296296297,
'incorrect buckling force after creation')
if __name__ == '__main__':
unittest.main()