conspire/domain/fem/block/element/linear/hexahedron/
mod.rs

1#[cfg(test)]
2mod test;
3
4use crate::{
5    fem::block::element::{
6        ElementNodalEitherCoordinates, FRAC_1_SQRT_3, FiniteElement, ParametricCoordinate,
7        ParametricCoordinates, ParametricReference, ShapeFunctions, ShapeFunctionsGradients,
8        linear::{LinearElement, LinearFiniteElement, M},
9    },
10    math::{ScalarList, Tensor, TensorArray},
11    mechanics::Coordinate,
12};
13
14const G: usize = 8;
15const N: usize = 8;
16const P: usize = N;
17
18const CORNERS: [[usize; 3]; N] = [
19    [1, 3, 4],
20    [2, 0, 5],
21    [3, 1, 6],
22    [0, 2, 7],
23    [7, 5, 0],
24    [4, 6, 1],
25    [5, 7, 2],
26    [6, 4, 3],
27];
28
29pub type Hexahedron = LinearElement<G, N>;
30
31impl FiniteElement<G, M, N, P> for Hexahedron {
32    fn integration_points() -> ParametricCoordinates<G, M> {
33        [
34            [-FRAC_1_SQRT_3, -FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
35            [-FRAC_1_SQRT_3, -FRAC_1_SQRT_3, FRAC_1_SQRT_3],
36            [-FRAC_1_SQRT_3, FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
37            [-FRAC_1_SQRT_3, FRAC_1_SQRT_3, FRAC_1_SQRT_3],
38            [FRAC_1_SQRT_3, -FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
39            [FRAC_1_SQRT_3, -FRAC_1_SQRT_3, FRAC_1_SQRT_3],
40            [FRAC_1_SQRT_3, FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
41            [FRAC_1_SQRT_3, FRAC_1_SQRT_3, FRAC_1_SQRT_3],
42        ]
43        .into()
44    }
45    fn integration_weights(&self) -> &ScalarList<G> {
46        &self.integration_weights
47    }
48    fn parametric_reference() -> ParametricReference<M, N> {
49        [
50            [-1.0, -1.0, -1.0],
51            [1.0, -1.0, -1.0],
52            [1.0, 1.0, -1.0],
53            [-1.0, 1.0, -1.0],
54            [-1.0, -1.0, 1.0],
55            [1.0, -1.0, 1.0],
56            [1.0, 1.0, 1.0],
57            [-1.0, 1.0, 1.0],
58        ]
59        .into()
60    }
61    fn parametric_weights() -> ScalarList<G> {
62        [1.0; G].into()
63    }
64    fn scaled_jacobians<const I: usize>(
65        nodal_coordinates: ElementNodalEitherCoordinates<I, N>,
66    ) -> ScalarList<P> {
67        let mut u = Coordinate::zero();
68        let mut v = Coordinate::zero();
69        let mut w = Coordinate::zero();
70        let mut n = Coordinate::zero();
71        CORNERS
72            .into_iter()
73            .enumerate()
74            .map(|(node, [node_a, node_b, node_c])| {
75                u = &nodal_coordinates[node_a] - &nodal_coordinates[node];
76                v = &nodal_coordinates[node_b] - &nodal_coordinates[node];
77                w = &nodal_coordinates[node_c] - &nodal_coordinates[node];
78                n = u.cross(&v);
79                (&n * &w) / u.norm() / v.norm() / w.norm()
80            })
81            .collect()
82    }
83    fn shape_functions(parametric_coordinate: ParametricCoordinate<M>) -> ShapeFunctions<N> {
84        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
85        [
86            (1.0 - xi_1) * (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
87            (1.0 + xi_1) * (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
88            (1.0 + xi_1) * (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
89            (1.0 - xi_1) * (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
90            (1.0 - xi_1) * (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
91            (1.0 + xi_1) * (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
92            (1.0 + xi_1) * (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
93            (1.0 - xi_1) * (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
94        ]
95        .into()
96    }
97    fn shape_functions_gradients(
98        parametric_coordinate: ParametricCoordinate<M>,
99    ) -> ShapeFunctionsGradients<M, N> {
100        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
101        [
102            [
103                -(1.0 - xi_2) * (1.0 - xi_3) / 8.0,
104                -(1.0 - xi_1) * (1.0 - xi_3) / 8.0,
105                -(1.0 - xi_1) * (1.0 - xi_2) / 8.0,
106            ],
107            [
108                (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
109                -(1.0 + xi_1) * (1.0 - xi_3) / 8.0,
110                -(1.0 + xi_1) * (1.0 - xi_2) / 8.0,
111            ],
112            [
113                (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
114                (1.0 + xi_1) * (1.0 - xi_3) / 8.0,
115                -(1.0 + xi_1) * (1.0 + xi_2) / 8.0,
116            ],
117            [
118                -(1.0 + xi_2) * (1.0 - xi_3) / 8.0,
119                (1.0 - xi_1) * (1.0 - xi_3) / 8.0,
120                -(1.0 - xi_1) * (1.0 + xi_2) / 8.0,
121            ],
122            [
123                -(1.0 - xi_2) * (1.0 + xi_3) / 8.0,
124                -(1.0 - xi_1) * (1.0 + xi_3) / 8.0,
125                (1.0 - xi_1) * (1.0 - xi_2) / 8.0,
126            ],
127            [
128                (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
129                -(1.0 + xi_1) * (1.0 + xi_3) / 8.0,
130                (1.0 + xi_1) * (1.0 - xi_2) / 8.0,
131            ],
132            [
133                (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
134                (1.0 + xi_1) * (1.0 + xi_3) / 8.0,
135                (1.0 + xi_1) * (1.0 + xi_2) / 8.0,
136            ],
137            [
138                -(1.0 + xi_2) * (1.0 + xi_3) / 8.0,
139                (1.0 - xi_1) * (1.0 + xi_3) / 8.0,
140                (1.0 - xi_1) * (1.0 + xi_2) / 8.0,
141            ],
142        ]
143        .into()
144    }
145}
146
147impl LinearFiniteElement<G, N> for Hexahedron {}
conspire/domain/fem/block/element/linear/hexahedron/mod.rs

conspire/domain/fem/block/element/linear/hexahedron/
mod.rs
