Cylindrical shells modeled as panel multidomain assemblies#
- panels.multidomain.cylinder.create_cylinder(height, r, stack, plyt, laminaprop, npanels, m=8, n=8)#
Create a cylinder multidomain assembly
The multidomain assembly looks like:
B A _______ _______ _______ _______ | | | | | | | | | | | | | | | | p04 | p03 | p02 | p01 | | | | | | /\ x | | | | | | |_______|_______|_______|_______| | | y <-------
where edges
AandBare connected to close the cylinder.- Parameters:
- heightfloat
Cylinder height (along \(x\)).
- rfloat
Cylinder radius.
- stacklist or tuple
Stacking sequence for the cylinder.
- plytfloat
Ply thickness.
- laminaproplist or tuple
Orthotropic lamina properties: \(E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}\).
- npanelsint
The number of panels the cylinder perimiter.
- m, nint, optional
Number of approximation terms for each panel.
- Returns:
- md, connstuple
A tuple containing the multidomain assembly and the default connectivity list of dictionaries.
Notes
The code of this function is illustrative of how it constructs the multidomain assembly:
def create_cylinder(height, r, stack, plyt, laminaprop, npanels, m=8, n=8): r"""Create a cylinder multidomain assembly The multidomain assembly looks like:: B A _______ _______ _______ _______ | | | | | | | | | | | | | | | | p04 | p03 | p02 | p01 | | | | | | /\ x | | | | | | |_______|_______|_______|_______| | | y <------- where edges ``A`` and ``B`` are connected to close the cylinder. Parameters ---------- height : float Cylinder height (along `x`). r : float Cylinder radius. stack : list or tuple Stacking sequence for the cylinder. plyt : float Ply thickness. laminaprop : list or tuple Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`. npanels : int The number of panels the cylinder perimiter. m, n : int, optional Number of approximation terms for each panel. Returns ------- md, conns : tuple A tuple containing the multidomain assembly and the default connectivity list of dictionaries. Notes ----- The code of this function is illustrative of how it constructs the multidomain assembly: .. literalinclude:: ../../panels/multidomain/cylinder.py :pyobject: create_cylinder """ if npanels < 2: raise ValueError('At least two panels are needed') skin = [] perimiter = 2*np.pi*r b_skin = perimiter / npanels for i in range(npanels): y0 = i*b_skin panel = Shell(group='skin', x0=0, y0=y0, a=height, b=b_skin, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, x1u=0, x1ur=1, x2u=0, x2ur=1, x1v=0, x1vr=1, x2v=0, x2vr=1, x1w=0, x1wr=1, x2w=0, x2wr=1, y1u=1, y1ur=1, y2u=1, y2ur=1, y1v=1, y1vr=1, y2v=1, y2vr=1, y1w=1, y1wr=1, y2w=1, y2wr=1) skin.append(panel) conns = [] skin_loop = skin + [skin[0]] for i in range(len(skin)): if i != len(skin) - 1: p01 = skin_loop[i] p02 = skin_loop[i+1] conns.append(dict(p1=p01, p2=p02, func='SSycte', ycte1=p01.b, ycte2=0)) else: p01 = skin_loop[i+1] p02 = skin_loop[i] conns.append(dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b)) md = MultiDomain(skin) return md, conns
- panels.multidomain.cylinder.cylinder_compression_lb_Nxx_cte(height, r, stack, plyt, laminaprop, npanels, Nxxs, m=8, n=8, num_eigvalues=20)#
Linear buckling analysis with a constant Nxx for each panel
See
create_cylinder()for most parameters.The cylinder has SS1 at the bottom and SS3 at the top. SS3 means that the edge is free to move in the axial direction.
- Parameters:
- Nxxslist
A Nxx for each panel.
- num_eigvaluesint
Number of eigenvalues to be extracted.
- Returns:
- md, eigvals, eigvecstuple
Assembly, eigenvalues and eigenvectors.
Examples
The following example is one of the test cases:
def test_cylinder_compression_lb_Nxx_cte(): print('Testing assembly function: cylinder_compression_lb_Nxx_cte') height = 0.500 r = 0.250 npanels = 5 Nxxs = [-100.]*npanels assy, eigvals, eigvecs = cylinder_compression_lb_Nxx_cte( height=height, r=r, plyt=0.125e-3, stack=[0, 45, -45, 90, -45, 45], laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9), npanels=npanels, Nxxs=Nxxs, m=8, n=12) assy.plot(eigvecs[:, 0], 'skin', filename='tmp_cylinder_compression_lb_Nxx_cte.png') assert np.isclose(Nxxs[0]*eigvals[0], -47319.181, atol=0.01, rtol=0.001)
- panels.multidomain.cylinder.cylinder_compression_lb_Nxx_from_static(height, r, stack, plyt, laminaprop, npanels, Nxxs, m=8, n=8, num_eigvalues=20)#
Linear buckling analysis with a Nxx calculated using static analysis
See
create_cylinder()for most parameters.The cylinder has SS1 at the bottom and SS3 at the top. SS3 means that the edge is free to move in the axial direction.
- Parameters:
- Nxxslist
A Nxx for each panel.
- num_eigvaluesint
Number of eigenvalues to be extracted.
- Returns:
- md, c, eigvals, eigvecstuple
Assembly, static results, eigenvalues and eigenvectors.
Examples
The following example is one of the test cases:
def test_cylinder_compression_lb_Nxx_from_static(): print('Testing assembly function: cylinder_compression_lb_Nxx_from_static') height = 0.500 r = 0.250 npanels = 5 Nxxs = [-100.]*npanels assy, c, eigvals, eigvecs = cylinder_compression_lb_Nxx_from_static( height=height, r=r, plyt=0.125e-3, stack=[0, 45, -45, 90, -45, 45], laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9), npanels=npanels, Nxxs=Nxxs, m=8, n=12) assy.plot(c, 'skin', filename='tmp_cylinder_compression_lb_Nxx_from_static_c.png') assy.plot(eigvecs[:, 0], 'skin', filename='tmp_cylinder_compression_lb_Nxx_from_static_eigvec.png') assert np.isclose(Nxxs[0]*eigvals[0], -47417.912, atol=0.01, rtol=0.001)
- panels.multidomain.cylinder_blade_stiffened.create_cylinder_blade_stiffened(height, r, stack, stack_blades, width_blades, plyt, laminaprop, npanels, m=8, n=8)#
Create a cylinder multidomain assembly with blade stiffeners
The multidomain assembly looks like:
B A _______ _______ _______ _______ | | | | | | | | | | | | | | | | p04 | p03 | p02 | p01 | | | | | | | | | | | |_______|_______|_______|_______| Blade Blade Blade Blade 04 03 02 01 _ _ _ _ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |_| |_| |_| |_| x /\ | | y <-------
where edges
AandBare connected to close de cylinder.- Parameters:
- heightfloat
Cylinder height (along \(x\)).
- rfloat
Cylinder radius.
- stackarray-like
Stacking sequence for the cylinder.
- stack_bladeslist of array-like
The stacking sequence for each blade (with length = npanels).
- width_bladesarray-like
The width for each blade (with length = npanels).
- plytfloat
Ply thickness (assumed unique for the whole structure).
- laminaproplist or tuple
Orthotropic lamina properties: \(E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}\).
- npanelsint
The number of panels the cylinder perimiter.
- m, nint, optional
Number of approximation terms for each panel.
- Returns:
- md, connstuple
A tuple containing the multidomain assembly and the default connectivity list of dictionaries.
Notes
The code of this function is illustrative of how it constructs the multidomain assembly:
def create_cylinder_blade_stiffened(height, r, stack, stack_blades, width_blades, plyt, laminaprop, npanels, m=8, n=8): r"""Create a cylinder multidomain assembly with blade stiffeners The multidomain assembly looks like:: B A _______ _______ _______ _______ | | | | | | | | | | | | | | | | p04 | p03 | p02 | p01 | | | | | | | | | | | |_______|_______|_______|_______| Blade Blade Blade Blade 04 03 02 01 _ _ _ _ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |_| |_| |_| |_| x /\ | | y <------- where edges ``A`` and ``B`` are connected to close de cylinder. Parameters ---------- height : float Cylinder height (along `x`). r : float Cylinder radius. stack : array-like Stacking sequence for the cylinder. stack_blades : list of array-like The stacking sequence for each blade (with length = npanels). width_blades : array-like The width for each blade (with length = npanels). plyt : float Ply thickness (assumed unique for the whole structure). laminaprop : list or tuple Orthotropic lamina properties: `E_1, E_2, \nu_{12}, G_{12}, G_{13}, G_{23}`. npanels : int The number of panels the cylinder perimiter. m, n : int, optional Number of approximation terms for each panel. Returns ------- md, conns : tuple A tuple containing the multidomain assembly and the default connectivity list of dictionaries. Notes ----- The code of this function is illustrative of how it constructs the multidomain assembly: .. literalinclude:: ../../panels/multidomain/cylinder_blade_stiffened.py :pyobject: create_cylinder_blade_stiffened """ if npanels < 2: raise ValueError('At least two panels are needed') if len(stack_blades) != npanels: raise ValueError('stack_blades must have length = npanels') if len(width_blades) != npanels: raise ValueError('width_blades must have length = npanels') skin = [] blades = [] perimiter = 2*np.pi*r b_skin = perimiter / npanels for i in range(npanels): y0 = i*b_skin panel = Shell(group='skin', x0=0, y0=y0, a=height, b=b_skin, r=r, m=m, n=n, plyt=plyt, stack=stack, laminaprop=laminaprop, x1u=0, x1ur=1, x2u=0, x2ur=1, x1v=0, x1vr=1, x2v=0, x2vr=1, x1w=0, x1wr=1, x2w=0, x2wr=1, y1u=1, y1ur=1, y2u=1, y2ur=1, y1v=1, y1vr=1, y2v=1, y2vr=1, y1w=1, y1wr=1, y2w=1, y2wr=1) skin.append(panel) for i, panel in enumerate(skin): y0 = i*b_skin blade_name = 'blade_%02d' % i blade = Shell(group=blade_name, x0=0, y0=y0, a=height, b=width_blades[i], m=m, n=n, plyt=plyt, stack=stack_blades[i], laminaprop=laminaprop, x1u=0, x1ur=1, x2u=0, x2ur=1, x1v=0, x1vr=1, x2v=0, x2vr=1, x1w=0, x1wr=1, x2w=0, x2wr=1, y1u=1, y1ur=1, y2u=1, y2ur=1, y1v=1, y1vr=1, y2v=1, y2vr=1, y1w=1, y1wr=1, y2w=1, y2wr=1) blades.append(blade) conns = [] skin_loop = skin + [skin[0]] for i in range(len(skin)): if i != len(skin) - 1: p01 = skin_loop[i] p02 = skin_loop[i+1] conns.append(dict(p1=p01, p2=p02, func='SSycte', ycte1=p01.b, ycte2=0)) else: p01 = skin_loop[i+1] p02 = skin_loop[i] conns.append(dict(p1=p01, p2=p02, func='SSycte', ycte1=0, ycte2=p02.b)) for panel, blade in zip(skin, blades): conns.append(dict(p1=panel, p2=blade, func='BFycte', ycte1=0, ycte2=0)) md = MultiDomain(skin + blades) return md, conns
- panels.multidomain.cylinder_blade_stiffened.cylinder_blade_stiffened_compression_lb_Nxx_cte(height, r, stack, stack_blades, width_blades, plyt, laminaprop, npanels, Nxxs_skin, Nxxs_blade, m=8, n=8, num_eigvalues=20)#
Linear buckling analysis with a constant Nxx for each panel
See
create_cylinder_blade_stiffened()for most parameters.- Parameters:
- Nxxs_skinlist
A Nxx for each skin panel.
- Nxxs_bladelist
A Nxx for each blade stiffener.
- num_eigvaluesint
Number of eigenvalues to be extracted.
- Returns:
- md, eigvals, eigvecstuple
Assembly, eigenvalues and eigenvectors.
Examples
The following example is one of the test cases:
def test_cylinder_blade_stiffened_compression_lb_Nxx_cte(): print('Testing assembly function: cylinder_blade_stiffened_compression_lb_Nxx_cte') height = 0.500 r = 0.250 npanels = 5 Nxxs = [-100.]*npanels assy, eigvals, eigvecs = cylinder_blade_stiffened_compression_lb_Nxx_cte( height=height, r=r, plyt=0.125e-3, stack=[0, 45, -45, 90, -45, 45], stack_blades=[[0, 90, 0]*4]*npanels, width_blades=[0.02]*npanels, laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9), npanels=npanels, Nxxs_skin=Nxxs, Nxxs_blade=Nxxs, m=8, n=12) assy.plot(eigvecs[:, 0], 'skin', filename='tmp_cylinder_blade_stiffened_compression_lb_Nxx_cte_eigvec.png') assert np.isclose(Nxxs[0]*eigvals[0], -51905.843, atol=0.01, rtol=0.001)
- panels.multidomain.cylinder_blade_stiffened.cylinder_blade_stiffened_compression_lb_Nxx_from_static(height, r, stack, stack_blades, width_blades, plyt, laminaprop, npanels, Nxxs_skin, Nxxs_blade, m=8, n=8, num_eigvalues=20)#
Linear buckling analysis with a Nxx calculated using static analysis
See
create_cylinder_blade_stiffened()for most parameters.- Parameters:
- Nxxs_skinlist
A Nxx for each skin panel.
- Nxxs_bladelist
A Nxx for each blade stiffener.
- num_eigvaluesint
Number of eigenvalues to be extracted.
- Returns:
- md, c, eigvals, eigvecstuple
Assembly, static results, eigenvalues and eigenvectors.
Examples
The following example is one of the test cases:
def test_cylinder_blade_stiffened_compression_lb_Nxx_from_static(): print('Testing assembly function: cylinder_blade_stiffened_compression_lb_Nxx_from_static') height = 0.500 r = 0.250 npanels = 5 Nxxs = [-100.]*npanels assy, c, eigvals, eigvecs = cylinder_blade_stiffened_compression_lb_Nxx_from_static( height=height, r=r, plyt=0.125e-3, stack=[0, 45, -45, 90, -45, 45], stack_blades=[[0, 90, 0]*4]*npanels, width_blades=[0.02]*npanels, laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9), npanels=npanels, Nxxs_skin=Nxxs, Nxxs_blade=Nxxs, m=8, n=12) assy.plot(c, 'skin', vec='u', filename='tmp_cylinder_blade_stiffened_compression_lb_Nxx_from_static_u.png', colorbar=True) assy.plot(c, 'skin', vec='w', filename='tmp_cylinder_blade_stiffened_compression_lb_Nxx_from_static_w.png', colorbar=True) assy.plot(c, 'skin', vec='Nxx', filename='tmp_cylinder_blade_stiffened_compression_lb_Nxx_from_static_Nxx.png', colorbar=True) assy.plot(c, 'skin', vec='Nyy', filename='tmp_cylinder_blade_stiffened_compression_lb_Nxx_from_static_Nyy.png', colorbar=True) assy.plot(eigvecs[:, 0], 'skin', filename='tmp_cylinder_blade_stiffened_compression_lb_Nxx_from_static_eigvec.png') assert np.isclose(Nxxs[0]*eigvals[0], -40003, atol=0.01, rtol=0.001)
- panels.multidomain.cylinder_blade_stiffened.cylinder_blade_stiffened_compression_lb_pd_from_static(height, r, stack, stack_blades, width_blades, plyt, laminaprop, npanels, pds_skin, pds_blade, m=8, n=8, num_eigvalues=20, ku=1000000.0)#
Linear buckling analysis with prescribed displacement
See
create_cylinder_blade_stiffened()for most parameters.- Parameters:
- pds_skinlist
A prescribed axial compression displacement for each skin panel.
- pds_bladelist
A prescribed axial compression displacement for each blade stiffener.
- num_eigvaluesint
Number of eigenvalues to be extracted.
- kufloat
Penalty stiffness used for prescribing displacements.
- Returns:
- md, c, eigvals, eigvecstuple
Assembly, static results, eigenvalues and eigenvectors.
Examples
The following example is one of the test cases:
def test_cylinder_blade_stiffened_compression_lb_pd_from_static(): print('Testing assembly function: cylinder_blade_stiffened_compression_lb_pd_from_static') height = 0.500 r = 0.250 npanels = 5 pds = [-1.e-3]*npanels assy, c, eigvals, eigvecs = cylinder_blade_stiffened_compression_lb_pd_from_static( height=height, r=r, plyt=0.125e-3, stack=[0, 45, -45, 90, -45, 45], stack_blades=[[0, 90, 0]*4]*npanels, width_blades=[0.02]*npanels, laminaprop=(142.5e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 5.1e9), npanels=npanels, pds_skin=pds, pds_blade=pds, m=8, n=12) assy.plot(c, 'skin', vec='u', filename='tmp_cylinder_blade_stiffened_compression_lb_pd_from_static_u.png', colorbar=True) assy.plot(c, 'skin', vec='w', filename='tmp_cylinder_blade_stiffened_compression_lb_pd_from_static_w.png', colorbar=True) assy.plot(c, 'skin', vec='Nxx', filename='tmp_cylinder_blade_stiffened_compression_lb_pd_from_static_Nxx.png', colorbar=True) assy.plot(c, 'skin', vec='Nyy', filename='tmp_cylinder_blade_stiffened_compression_lb_pd_from_static_Nyy.png', colorbar=True) assy.plot(eigvecs[:, 0], 'skin', filename='tmp_cylinder_blade_stiffened_compression_lb_pd_from_static_eigvec.png')