9.3  Mesh Class

Initialization

A Mesh object is created by providing nodal coordinates and element connectivity.

Signature:

class Mesh(node_coords, element_connectivity, 
           element_type=None, dofs_per_node=None)

Parameters:

• node_coords (array-like): An array of shape (n_nodes, n_dim) containing the coordinates of each node.
• element_connectivity (array-like): An array of shape (n_elements, nodes_per_element) that defines which nodes belong to each element. This must use 1-based node numbers.
• element_type (str, optional): The type of element (e.g., 'ROD', 'TRIA3'). If not provided, it will be auto-detected based on the number of nodes per element.
• dofs_per_node (int, optional): The number of degrees of freedom per node. If not provided, it is inferred from the element type and dimension.

Example:

import numpy as np
from mechanicskit import Mesh

coords = np.array([[0, 0], 
                  [1, 0], 
                  [0, 1]])
# A single triangle connecting nodes 1, 2, and 3
elements = np.array([[1, 2, 3]]) 

mesh = Mesh(coords, elements) # Auto-detects 'TRIA3'
mesh

Mesh(element_type='TRIA3', n_nodes=3, n_elements=1, n_dim=2D, dofs_per_node=2)

Properties

You can access basic information about the mesh through its properties.

• mesh.nodes: Returns the full (n_nodes, n_dim) NumPy array of node coordinates.
• mesh.elements: Returns the (n_elements, nodes_per_element) NumPy array of element connectivity, using 1-based node numbers.
• mesh.connectivity: An alias for mesh.elements.
• mesh.n_nodes: The total number of nodes.
• mesh.n_elements: The total number of elements.
• mesh.n_dim: The spatial dimension of the mesh (2 for 2D, 3 for 3D).
• mesh.element_type: The detected or specified element type.
• mesh.dofs_per_node: The number of degrees of freedom at each node.
• mesh.n_dofs: The total number of degrees of freedom in the mesh.

Summary

mesh.summary()

Mesh Summary
============================================================
Element type:       TRIA3 - 2D triangular element
Number of nodes:    3
Number of elements: 1
Dimension:          2D
DOFs per node:      2
Total DOFs:         6

Node Coordinates (1-based numbering):
------------------------------------------------------------
  Node 1: [0. 0.]
  Node 2: [1. 0.]
  Node 3: [0. 1.]

Element Connectivity (1-based numbering):
------------------------------------------------------------
  Element 1: Nodes [np.int64(1), np.int64(2), np.int64(3)]

Accessing Data

These methods allow you to retrieve information about specific nodes or elements using 1-based numbering.

# Get coordinates of node 3
coords_3 = mesh.get_node(3)

# Get coordinates of nodes 1 and 3
coords_1_3 = mesh.get_node([1, 3])

node_nums, coords = mesh.get_element(1)

DOF Management

# For a 2D mesh, node 3 has DOFs 5 and 6 (in 1-based math)
# The method returns the 0-based indices for array access.
dofs = mesh.dofs_for_node(3)
# dofs is now array([4, 5])

# Use this to access a global displacement vector `u_global`
displacement_at_node_3 = u_global[dofs]

Iterators

For clean, readable loops, the Mesh class provides iterators that yield 1-based numbers.

• mesh.element_numbers(): Yields element numbers from 1 to n_elements.
• mesh.node_numbers(): Yields node numbers from 1 to n_nodes.
• mesh.iter_elements(): Yields a tuple (elem_number, node_numbers, coords) for each element.
• mesh.iter_nodes(): Yields a tuple (node_number, coords) for each node.

Example:

# Calculate the length of each element
for iel, node_nums, coords in mesh.iter_elements():
    length = np.linalg.norm(coords[1] - coords[0])
    print(f"Element {iel} has length {length:.2f}")

Element 1 has length 1.00

Field Management

These methods allow you to associate data fields (like forces or temperatures) with the mesh and access them using 1-based indexing via the OneArray wrapper.

temps = mesh.Add_Nodal_Field('temperature', [20.0, 25.0, 30.0])
print(temps[2]) # Access temperature at node 2

25.0

forces = mesh.Add_Element_Field('forces', [100.0])
print(forces[1]) # Access force in element 1

100.0