Tri6#
- class sectionproperties.analysis.fea.Tri6(el_id: int, coords: npt.NDArray[np.float64], node_ids: list[int], material: Material)[source]#
Bases:
object
Class for a six-node quadratic triangular element.
Provides methods for the calculation of section properties based on the finite element method.
- Parameters:
el_id (int) – Unique element id
coords (numpy.ndarray) – A
2 x 6
array of the coordinates of the Tri6 nodes. The first three columns relate to the vertices of the triangle and the last three columns correspond to the mid-nodes.node_ids (list[int]) – A list of the global node ids for the current element
material (Material) – Material object for the current finite element
Methods
Calculates the stress within an element resulting from a specified loading.
Calculates the geometric properties for the current finite element.
Maps a global point onto a local point.
Calculates the stress at a point resulting from a specified loading.
Calculates the integrals used to evaluate the monosymmetry constants.
Determines whether a point lies within the current element.
Calculates the variables used to for the shear deformation coefficients.
Calculates the element shear load vectors for evaluating the shear functions.
Calculates the element shear centre and warping integrals for shear analysis.
Calculates the element warping stiffness matrix and the torsion load vector.
Attributes
el_id
coords
node_ids
material
- geometric_properties() tuple[float, float, float, float, float, float, float, float, float] [source]#
Calculates the geometric properties for the current finite element.
- torsion_properties() tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]] [source]#
Calculates the element warping stiffness matrix and the torsion load vector.
- shear_load_vectors(ixx: float, iyy: float, ixy: float, nu: float) tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]] [source]#
Calculates the element shear load vectors for evaluating the shear functions.
- shear_warping_integrals(ixx: float, iyy: float, ixy: float, omega: ndarray[Any, dtype[float64]]) tuple[float, float, float, float, float, float] [source]#
Calculates the element shear centre and warping integrals for shear analysis.
- Parameters:
- Returns:
Shear centre integrals about the
x
andy
axes and warping integrals (sc_xint
,sc_yint
,q_omega
,i_omega
,i_xomega
,i_yomega
)- Return type:
- shear_coefficients(ixx: float, iyy: float, ixy: float, psi_shear: ndarray[Any, dtype[float64]], phi_shear: ndarray[Any, dtype[float64]], nu: float) tuple[float, float, float] [source]#
Calculates the variables used to for the shear deformation coefficients.
- Parameters:
ixx (float) – Second moment of area about the centroidal x-axis
iyy (float) – Second moment of area about the centroidal y-axis
ixy (float) – Second moment of area about the centroidal xy-axis
psi_shear (ndarray[Any, dtype[float64]]) – Values of the psi shear function at the element nodes
phi_shear (ndarray[Any, dtype[float64]]) – Values of the phi shear function at the element nodes
nu (float) – Effective Poisson’s ratio for the cross-section
- Returns:
Shear deformation variables (
kappa_x
,kappa_y
,kappa_xy
)- Return type:
- monosymmetry_integrals(phi: float) tuple[float, float, float, float] [source]#
Calculates the integrals used to evaluate the monosymmetry constants.
- element_stress(n: float, mxx: float, myy: float, m11: float, m22: float, mzz: float, vx: float, vy: float, ea: float, cx: float, cy: float, ixx: float, iyy: float, ixy: float, i11: float, i22: float, phi: float, j: float, nu: float, omega: ndarray[Any, dtype[float64]], psi_shear: ndarray[Any, dtype[float64]], phi_shear: ndarray[Any, dtype[float64]], delta_s: float) tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]] [source]#
Calculates the stress within an element resulting from a specified loading.
- Parameters:
n (float) – Axial force
mxx (float) – Bending moment about the centroidal xx-axis
myy (float) – Bending moment about the centroidal yy-axis
m11 (float) – Bending moment about the centroidal 11-axis
m22 (float) – Bending moment about the centroidal 22-axis
mzz (float) – Torsion moment about the centroidal zz-axis
vx (float) – Shear force acting in the x-direction
vy (float) – Shear force acting in the y-direction
ea (float) – Modulus weighted area
cx (float) – x position of the elastic centroid
cy (float) – y position of the elastic centroid
ixx (float) – Second moment of area about the centroidal x-axis
iyy (float) – Second moment of area about the centroidal y-axis
ixy (float) – Second moment of area about the centroidal xy-axis
i11 (float) – Second moment of area about the principal 11-axis
i22 (float) – Second moment of area about the principal 22-axis
phi (float) – Principal bending axis angle
j (float) – St. Venant torsion constant
nu (float) – Effective Poisson’s ratio for the cross-section
omega (ndarray[Any, dtype[float64]]) – Values of the warping function at the element nodes
psi_shear (ndarray[Any, dtype[float64]]) – Values of the psi shear function at the element nodes
phi_shear (ndarray[Any, dtype[float64]]) – Values of the phi shear function at the element nodes
delta_s (float) – Cross-section shear factor
- Returns:
Tuple containing element stresses and integration weights (\(\sigma_{zz,n}\), \(\sigma_{zz,mxx}\), \(\sigma_{zz,myy}\), \(\sigma_{zz,m11}\), \(\sigma_{zz,m22}\), \(\sigma_{zx,mzz}\), \(\sigma_{zy,mzz}\), \(\sigma_{zx,vx}\), \(\sigma_{zy,vx}\), \(\sigma_{zx,vy}\), \(\sigma_{zy,vy}\), \(w_i\))
- Return type:
tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]]
- local_element_stress(p: tuple[float, float], n: float, mxx: float, myy: float, m11: float, m22: float, mzz: float, vx: float, vy: float, ea: float, cx: float, cy: float, ixx: float, iyy: float, ixy: float, i11: float, i22: float, phi: float, j: float, nu: float, omega: ndarray[Any, dtype[float64]], psi_shear: ndarray[Any, dtype[float64]], phi_shear: ndarray[Any, dtype[float64]], delta_s: float) tuple[float, float, float] [source]#
Calculates the stress at a point resulting from a specified loading.
- Parameters:
p (tuple[float, float]) – Point (
x
,y
) in the global coordinate system that is within the elementn (float) – Axial force
mxx (float) – Bending moment about the centroidal xx-axis
myy (float) – Bending moment about the centroidal yy-axis
m11 (float) – Bending moment about the centroidal 11-axis
m22 (float) – Bending moment about the centroidal 22-axis
mzz (float) – Torsion moment about the centroidal zz-axis
vx (float) – Shear force acting in the x-direction
vy (float) – Shear force acting in the y-direction
ea (float) – Modulus weighted area
cx (float) – x position of the elastic centroid
cy (float) – y position of the elastic centroid
ixx (float) – Second moment of area about the centroidal x-axis
iyy (float) – Second moment of area about the centroidal y-axis
ixy (float) – Second moment of area about the centroidal xy-axis
i11 (float) – Second moment of area about the principal 11-axis
i22 (float) – Second moment of area about the principal 22-axis
phi (float) – Principal bending axis angle
j (float) – St. Venant torsion constant
nu (float) – Effective Poisson’s ratio for the cross-section
omega (ndarray[Any, dtype[float64]]) – Values of the warping function at the element nodes
psi_shear (ndarray[Any, dtype[float64]]) – Values of the psi shear function at the element nodes
phi_shear (ndarray[Any, dtype[float64]]) – Values of the phi shear function at the element nodes
delta_s (float) – Cross-section shear factor
- Returns:
Tuple containing stress values at point
p
(\(\sigma_{zz}\), \(\sigma_{zx}\), \(\sigma_{zy}\))- Return type: