Spring - 3D spring element with constant stiffnesses (`pyfe3d.spring`)#

class pyfe3d.spring.Spring#

Spring 3D beam element with constant stiffnesses

Note

The default behaviour assumes that the local coordinate system is aligned with the global coordinate system

Attributes:

eid,int: Element identification number.
kxe, kye, kze: double: Translational stiffnesses in the element coordinate system.
krxe, krye, krzedouble: Rotational stiffnesses in the element coordinate system.
r11, r12, r13, r21, r22, r23, r31, r32, r33double: Rotation matrix from local to global coordinates. By default it assumes that the element is aligned with the global coordinate system.
vxyi, vxyj, vxykdouble: Components of a vector on the \(XY\) plane of the element coordinate system, defined using global coordinates.
c1, c2int: Position of each node in the global stiffness matrix.
n1, n2int: Node identification number.
init_k_KC0, init_k_KG, init_k_Mint: Position in the arrays storing the sparse data for the structural matrices.

Methods

`update_KC0`(self, long[, long[, double[, ...)	Update sparse vectors for linear constitutive stiffness matrix KC0
`update_probe_ue`(self, double[)	Update the local displacement vector of the probe of the element
`update_rotation_matrix`(self, double xi, ...)	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_KG#: init_k_KG: ‘int’

init_k_M#: init_k_M: ‘int’

krxe#: krxe: ‘double’

krye#: krye: ‘double’

krze#: krze: ‘double’

kxe#: kxe: ‘double’

kye#: kye: ‘double’

kze#: kze: ‘double’

n1#: n1: ‘int’

n2#: n2: ‘int’

probe#: probe: pyfe3d.spring.SpringProbe

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

Update the local displacement vector of the probe of the element

Note

The probe attribute object SpringProbe is updated, not the element object.

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_rotation_matrix(self, double xi, double xj, double xk, double vxyi, double vxyj, double vxyk) → 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:

xi, xj, xkdouble: Components, in global coordinates, of the element x-axis.
vxyi, vxyj, vxykdouble: Components, in global coordinates, of a vector on the \(XY\) plane of the element coordinate system.

vxyi#: vxyi: ‘double’

vxyj#: vxyj: ‘double’

vxyk#: vxyk: ‘double’

class pyfe3d.spring.SpringData#

Used to allocate memory for the sparse matrices.

Attributes:

KC0_SPARSE_SIZE,int: KC0_SPARSE_SIZE = 72
KG_SPARSE_SIZE,int: KG_SPARSE_SIZE = 0
M_SPARSE_SIZE,int: M_SPARSE_SIZE = 0

KC0_SPARSE_SIZE#: KC0_SPARSE_SIZE: ‘int’

KG_SPARSE_SIZE#: KG_SPARSE_SIZE: ‘int’

M_SPARSE_SIZE#: M_SPARSE_SIZE: ‘int’

class pyfe3d.spring.SpringProbe#

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

Attributes:

xe,array-like: Array of size NUM_NODES*DOF//2=6 containing the nodal coordinates in the element coordinate system, in the following order \({x_e}_1, {y_e}_1, {z_e}_1, {x_e}_2, {y_e}_2, {z_e}_2\).
ue,array-like: Array of size NUM_NODES*DOF=12 containing the element displacements in the following order \({u_e}_1, {v_e}_1, {w_e}_1, {{r_x}_e}_1, {{r_y}_e}_1, {{r_z}_e}_1, {u_e}_2, {v_e}_2, {w_e}_2, {{r_x}_e}_2, {{r_y}_e}_2, {{r_z}_e}_2\).

ue#: ue: ‘double[::1]’

xe#: xe: ‘double[::1]’

Spring - 3D spring element with constant stiffnesses (pyfe3d.spring)#

Spring - 3D spring element with constant stiffnesses (`pyfe3d.spring`)#