finite_element_method 0.9.12

A finite element method module.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113

use extended_matrix::{FloatTrait, Vector3, VectorTrait};

use std::collections::HashMap;

use crate::fem::math_functions::{derivative_x, power_func_x};
use crate::fem::structs::Node;

pub fn find_2n_element_vector<V>(
    node_1_number: u32,
    node_2_number: u32,
    nodes: &HashMap<u32, Node<V>>,
) -> Result<Vector3<V>, String>
where
    V: FloatTrait<Output = V>,
{
    let node_1 = nodes
        .get(&node_1_number)
        .ok_or(format!("Node {node_1_number} does not exist!"))?;
    let node_2 = nodes
        .get(&node_2_number)
        .ok_or(format!("Node {node_2_number} does not exist!"))?;

    let truss_element_vector_components: [V; 3] = node_2
        .get_coordinates()
        .iter()
        .zip(node_1.get_coordinates())
        .map(|(n_2, n_1)| *n_2 - n_1)
        .collect::<Vec<V>>()
        .try_into()
        .map_err(|e| format!("{e:?} could not be converted to arr[3]"))?;

    Ok(Vector3::create(&truss_element_vector_components))
}

fn dx_dr<V>(x_1: V, x_2: V, r: V) -> V
where
    V: FloatTrait<Output = V>,
{
    derivative_x(power_func_x, x_1 * V::from(0.5f32), V::from(0f32), 0)
        - derivative_x(power_func_x, x_1 * V::from(0.5f32), r, 1)
        + derivative_x(power_func_x, x_2 * V::from(0.5f32), V::from(0f32), 0)
        + derivative_x(power_func_x, x_2 * V::from(0.5f32), r, 1)
}

fn jacobian_at_r<V>(
    node_1_number: u32,
    node_2_number: u32,
    r: V,
    nodes: &HashMap<u32, Node<V>>,
) -> Result<V, String>
where
    V: FloatTrait<Output = V>,
{
    let bar_2n_element_vector = find_2n_element_vector(node_1_number, node_2_number, nodes)?;
    let bar_2n_element_length = bar_2n_element_vector.norm()?;
    let x_1 = V::from(-1f32) * bar_2n_element_length / V::from(2f32);
    let x_2 = bar_2n_element_length / V::from(2f32);
    Ok(dx_dr(x_1, x_2, r))
}

pub fn inverse_jacobian_at_r<V>(
    node_1_number: u32,
    node_2_number: u32,
    r: V,
    nodes: &HashMap<u32, Node<V>>,
) -> Result<V, String>
where
    V: FloatTrait<Output = V>,
{
    Ok(V::from(1f32) / jacobian_at_r(node_1_number, node_2_number, r, nodes)?)
}

pub fn determinant_of_jacobian_at_r<V>(
    node_1_number: u32,
    node_2_number: u32,
    r: V,
    nodes: &HashMap<u32, Node<V>>,
) -> Result<V, String>
where
    V: FloatTrait<Output = V>,
{
    jacobian_at_r(node_1_number, node_2_number, r, nodes)
}

pub fn h1_r<V>(r: V) -> V
where
    V: FloatTrait<Output = V>,
{
    V::from(0.5f32) * (V::from(1f32) - r)
}

pub fn h2_r<V>(r: V) -> V
where
    V: FloatTrait<Output = V>,
{
    V::from(0.5f32) * (V::from(1f32) + r)
}

pub fn dh1_dr<V>(r: V) -> V
where
    V: FloatTrait<Output = V>,
{
    derivative_x(power_func_x, V::from(0.5f32), V::from(0f32), 0)
        - derivative_x(power_func_x, V::from(0.5f32), r, 1)
}

pub fn dh2_dr<V>(r: V) -> V
where
    V: FloatTrait<Output = V>,
{
    derivative_x(power_func_x, V::from(0.5f32), V::from(0f32), 0)
        + derivative_x(power_func_x, V::from(0.5f32), r, 1)
}