Truss - Linear truss 3D element with analytical integration (`pyfe3d.truss`)#

Note

The BeamC element is recommended because of the better physical representation.

Note

The Truss element does not support linear buckling analysis.

class pyfe3d.truss.Truss#

Truss 3D element for axial- and torsion-only behavior

Nodal connectivity for the truss element:

______   --> u  ->>- rx
1    2

Note

The BeamC is recommended because of the better physical representation.

Attributes:

eid,int: Element identification number.
pid,int: Property identification number.
length,double: Element length.
r11, r12, r13, r21, r22, r23, r31, r32, r33double: Rotation matrix from local to global coordinates.
c1, c2int: Position of each node in the global stiffness matrix.
n1, n2int: Node identification number.
init_k_KC0, init_k_Mint: Position in the arrays storing the sparse data for the structural matrices.
probe,TrussProbe object: Pointer to the probe.

Methods

`update_KC0`(self, long[, long[, double[, ...)	Update sparse vectors for linear constitutive stiffness matrix KC0
`update_M`(self, long[, long[, double[, ...)	Update sparse vectors for mass matrix M
`update_fint`(self, double[, BeamProp prop)	Update the internal force vector
`update_length`(self)	Update element length
`update_probe_finte`(self, BeamProp prop)	Update the internal force vector of the probe
`update_probe_ue`(self, double[)	Update the local displacement vector of the probe of the element
`update_probe_xe`(self, double[)	Update the 3D coordinates of the probe of the element
`update_rotation_matrix`(self, double[)	Update the rotation matrix of the element

c1#: c1: ‘int’

c2#: c2: ‘int’

eid#: eid: ‘int’

init_k_KC0#: init_k_KC0: ‘int’

init_k_M#: init_k_M: ‘int’

length#: length: ‘double’

n1#: n1: ‘int’

n2#: n2: ‘int’

pid#: pid: ‘int’

probe#: probe: pyfe3d.truss.TrussProbe

r11#: r11: ‘double’

r12#: r12: ‘double’

r13#: r13: ‘double’

r21#: r21: ‘double’

r22#: r22: ‘double’

r23#: r23: ‘double’

r31#: r31: ‘double’

r32#: r32: ‘double’

r33#: r33: ‘double’

update_KC0(self, long[::1] KC0r, long[::1] KC0c, double[::1] KC0v, BeamProp prop, int update_KC0v_only=0) → void#

Update sparse vectors for linear constitutive stiffness matrix KC0

Parameters:

KC0rnp.array: Array to store row positions of sparse values
KC0cnp.array: Array to store column positions of sparse values
KC0vnp.array: Array to store sparse values
propBeamProp object: Beam property object from where the stiffness and mass attributes are read from.
update_KC0v_onlyint: The default 0 means that the row and column indices KC0r and KC0c should also be updated. Any other value will only update the stiffness matrix values KC0v.

update_M(self, long[::1] Mr, long[::1] Mc, double[::1] Mv, BeamProp prop, int mtype=0) → void#

Update sparse vectors for mass matrix M

For the Truss element, the inertial terms intrho, intrhoy, intrhoz, intrhoy2 and intrhoz2 of the beam property are important.

Parameters:

Mrnp.array: Array to store row positions of sparse values
Mcnp.array: Array to store column positions of sparse values
Mvnp.array: Array to store sparse values
mtypeint, optional: 0 for consistent mass matrix using method from Brockman 1987 1 for lumped mass matrix using method from Brockman 1987

update_fint(self, double[::1] fint, BeamProp prop) → void#

Update the internal force vector

Parameters:

fintnp.array: Array that is updated in place with the internal forces. The internal forces stored in fint are calculated in global coordinates. Method update_probe_finte() is called to update the parameter finte of the TrussProbe with the internal forces in local coordinates.
propBeamProp object: Beam property object from where the stiffness and mass attributes are read from.

update_length(self) → void#: Update element length

update_probe_finte(self, BeamProp prop) → void#

Update the internal force vector of the probe

The attribute finte is updated with the TrussProbe the internal forces in local coordinates. While using this function, mind that the probe can be shared amongst more than one finite element, depending how you defined them, meaning that the probe will always safe the values from the last udpate.

Note

The finte attribute of object TrussProbe is updated, accessible using .probe.finte.

Parameters:

propBeamProp object: Beam property object from where the stiffness and mass attributes are read from.

update_probe_ue(self, double[::1] u) → void#

Update the local displacement vector of the probe of the element

Note

The ue attribute of object TrussProbe is updated, accessible using .probe.ue.

Parameters:

uarray-like: Array with global displacements, for a total of \(M\) nodes in the model, this array will be arranged as: \(u_1, v_1, w_1, {r_x}_1, {r_y}_1, {r_z}_1, u_2, v_2, w_2, {r_x}_2, {r_y}_2, {r_z}_2, ..., u_M, v_M, w_M, {r_x}_M, {r_y}_M, {r_z}_M\).

update_probe_xe(self, double[::1] x) → void#

Update the 3D coordinates of the probe of the element

Note

The xe attribute of object TrussProbe is updated, accessible using .probe.xe.

Parameters:

xarray-like: Array with global nodal coordinates, for a total of \(M\) nodes in the model, this array will be arranged as: \(x_1, y_1, z_1, x_2, y_2, z_2, ..., x_M, y_M, z_M\).

update_rotation_matrix(self, double[::1] x) → void#

Update the rotation matrix of the element

Attributes r11,r12,r13,r21,r22,r23,r31,r32,r33 are updated, corresponding to the rotation matrix from local to global coordinates.

The element coordinate system is determined, identifying the \(ijk\) components of each axis: \({x_e}_i, {x_e}_j, {x_e}_k\); \({y_e}_i, {y_e}_j, {y_e}_k\); \({z_e}_i, {z_e}_j, {z_e}_k\).

Parameters:

xarray-like: Array with global nodal coordinates, for a total of \(M\) nodes in the model, this array will be arranged as: \(x_1, y_1, z_1, x_2, y_2, z_2, ..., x_M, y_M, z_M\).

class pyfe3d.truss.TrussData#

Used to allocate memory for the sparse matrices.

Attributes:

KC0_SPARSE_SIZEint: KC0_SPARSE_SIZE: ‘int’
M_SPARSE_SIZEint: M_SPARSE_SIZE: ‘int’

KC0_SPARSE_SIZE#: KC0_SPARSE_SIZE: ‘int’

M_SPARSE_SIZE#: M_SPARSE_SIZE: ‘int’

class pyfe3d.truss.TrussProbe#

Probe used for local coordinates, local displacements, local stresses etc

The idea behind using a probe is to avoid allocating larger memory buffers per finite element. The memory buffers are allocated per probe, and one probe can be shared amongst many finite elements, with the information being updated and retrieved on demand.

Note

The probe can be shared amongst more than one finite element, depending on how you defined them. Mind that the probe will always safe the values from the last udpate.

Attributes:

xearray-like: xe: ‘double[::1]’
uearray-like: ue: ‘double[::1]’
finte,array-like: Array of size NUM_NODES*DOF=12 containing the element internal forces corresponding to the degrees-of-freedom described by ue.

finte#: finte: ‘double[::1]’

ue#: ue: ‘double[::1]’

xe#: xe: ‘double[::1]’

Truss - Linear truss 3D element with analytical integration (pyfe3d.truss)#

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Truss - Linear truss 3D element with analytical integration (`pyfe3d.truss`)#