conspire/domain/fem/block/element/surface/linear/quadrilateral/
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        surface::{M, linear::LinearSurfaceElement},
9    },
10    math::{ScalarList, Tensor, TensorArray},
11    mechanics::Coordinate,
12};
13
14const G: usize = 4;
15const N: usize = 4;
16const P: usize = N;
17
18const CORNERS: [[usize; 2]; N] = [[1, 3], [2, 0], [3, 1], [0, 2]];
19
20pub type Quadrilateral = LinearSurfaceElement<G, N>;
21
22impl FiniteElement<G, M, N, P> for Quadrilateral {
23    fn integration_points() -> ParametricCoordinates<G, M> {
24        [
25            [-FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
26            [FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
27            [FRAC_1_SQRT_3, FRAC_1_SQRT_3],
28            [-FRAC_1_SQRT_3, FRAC_1_SQRT_3],
29        ]
30        .into()
31    }
32    fn integration_weights(&self) -> &ScalarList<G> {
33        &self.integration_weights
34    }
35    fn parametric_reference() -> ParametricReference<M, N> {
36        [[-1.0, -1.0], [1.0, -1.0], [1.0, 1.0], [-1.0, 1.0]].into()
37    }
38    fn parametric_weights() -> ScalarList<G> {
39        [1.0; G].into()
40    }
41    fn scaled_jacobians<const I: usize>(
42        nodal_coordinates: ElementNodalEitherCoordinates<I, N>,
43    ) -> ScalarList<P> {
44        let mut u = Coordinate::zero();
45        let mut v = Coordinate::zero();
46        let mut n = Coordinate::zero();
47        let x = (&nodal_coordinates[1] - &nodal_coordinates[0])
48            + (&nodal_coordinates[2] - &nodal_coordinates[3]);
49        let y = (&nodal_coordinates[2] - &nodal_coordinates[1])
50            + (&nodal_coordinates[3] - &nodal_coordinates[0]);
51        let nc = x.cross(&y).normalized();
52        CORNERS
53            .into_iter()
54            .enumerate()
55            .map(|(node, [node_a, node_b])| {
56                u = &nodal_coordinates[node_a] - &nodal_coordinates[node];
57                v = &nodal_coordinates[node_b] - &nodal_coordinates[node];
58                n = u.cross(&v);
59                (&n * &nc) / u.norm() / v.norm()
60            })
61            .collect()
62    }
63    fn shape_functions(parametric_coordinate: ParametricCoordinate<M>) -> ShapeFunctions<N> {
64        let [xi_1, xi_2] = parametric_coordinate.into();
65        [
66            (1.0 - xi_1) * (1.0 - xi_2) / 4.0,
67            (1.0 + xi_1) * (1.0 - xi_2) / 4.0,
68            (1.0 + xi_1) * (1.0 + xi_2) / 4.0,
69            (1.0 - xi_1) * (1.0 + xi_2) / 4.0,
70        ]
71        .into()
72    }
73    fn shape_functions_gradients(
74        parametric_coordinate: ParametricCoordinate<M>,
75    ) -> ShapeFunctionsGradients<M, N> {
76        let [xi_1, xi_2] = parametric_coordinate.into();
77        [
78            [-(1.0 - xi_2) / 4.0, -(1.0 - xi_1) / 4.0],
79            [(1.0 - xi_2) / 4.0, -(1.0 + xi_1) / 4.0],
80            [(1.0 + xi_2) / 4.0, (1.0 + xi_1) / 4.0],
81            [-(1.0 + xi_2) / 4.0, (1.0 - xi_1) / 4.0],
82        ]
83        .into()
84    }
85}
conspire/domain/fem/block/element/surface/linear/quadrilateral/mod.rs

conspire/domain/fem/block/element/surface/linear/quadrilateral/
mod.rs
