import numpy as np
def assemble_global_kinematic_matrix(element_stiffness_matrix, element_connectivity, num_nodes, num_dofs):
"""Assemble the global kinematic matrix for a 3D beam element.
Args:
element_stiffness_matrix: The 6x6 element stiffness matrix for the beam element.
element_connectivity: A list of the node IDs for the two nodes connected by the beam element.
num_nodes: The total number of nodes in the model.
num_dofs: The total number of degrees of freedom per node in the model.
Returns:
The global kinematic matrix as a NumPy array.
"""
# Initialize the global kinematic matrix to zero
global_kinematic_matrix = np.zeros((num_nodes * num_dofs, num_nodes * num_dofs))
# Get the node IDs and degrees of freedom for the two nodes connected by the beam element
node_1_id = element_connectivity[0]
node_2_id = element_connectivity[1]
dofs_1 = np.arange(num_dofs * node_1_id, num_dofs * (node_1_id + 1))
dofs_2 = np.arange(num_dofs * node_2_id, num_dofs * (node_2_id + 1))
# Assemble the global kinematic matrix using the element stiffness matrix
global_kinematic_matrix[np.ix_(dofs_1, dofs_1)] += element_stiffness_matrix[0:num_dofs, 0:num_dofs]
global_kinematic_matrix[np.ix_(dofs_1, dofs_2)] += element_stiffness_matrix[0:num_dofs, num_dofs:]
global_kinematic_matrix[np.ix_(dofs_2, dofs_1)] += element_stiffness_matrix[num_dofs:, 0:num_dofs]
global_kinematic_matrix[np.ix_(dofs_2, dofs_2)] += element_stiffness_matrix[num_dofs:, num_dofs:]
return global_kinematic_matrix
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