gemlab 2.0.0

Geometry and meshes laboratory for finite element analyses
Documentation 
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use russell_lab::{Matrix, Vector};

/// Defines a triangle with 15 nodes (quartic edges; interior nodes)
///
/// ![tri15](https://raw.githubusercontent.com/cpmech/gemlab/main/data/figures/test_draw_shape_tri15.svg)
///
/// # Local IDs of nodes
///
/// ```text
///  s
///  |
///  2, (0,1)
///  | ',
///  |   ',
/// 10     9,
///  |       ',
///  |         ',
///  5    14     4,
///  |             ',
///  |               ',
/// 11    12    13     8,
///  |                   ',
///  |(0,0)                ', (1,0)
///  0-----6-----3-----7-----1 ---- r
/// ```
///
/// # Local IDs of edges
///
/// ```text
///    2,
///    | ',
///    |   ',                p0  p1 p2 p3  p4
///   10     9,          e:0 [1, 0, 3,  7,  6]
///    |       ',        e:1 [2, 1, 4,  9,  8]
///    |         ', 1    e:2 [0, 2, 5, 11, 10]
/// 2  5    14     4,
///    |             ',
///    |               ',
///   11    12    13     8,
///    |                   ',
///    |                     ',
///    0-----6-----3-----7-----1
///                0
/// ```
///
/// # Notes
///
/// * The order of edge nodes is such that the normals are outward
/// * The order of edge nodes corresponds to [super::Lin5] nodes
/// * This shape is a higher-order version of [super::Tri6]
pub struct Tri15 {}

impl Tri15 {
    pub const GEO_NDIM: usize = 2;
    pub const NNODE: usize = 15;
    pub const NEDGE: usize = 3;
    pub const NFACE: usize = 0;
    pub const EDGE_NNODE: usize = 5;
    pub const FACE_NNODE: usize = 0;
    pub const FACE_NEDGE: usize = 0;
    pub const N_INTERIOR_NODE: usize = 3;
    pub const TRIANGULATE_NTRIANGLE: usize = 16;

    #[rustfmt::skip]
    pub const EDGE_NODE_IDS: [[usize; Tri15::EDGE_NNODE]; Tri15::NEDGE] = [
        [1, 0, 3,  7,  6],
        [2, 1, 4,  9,  8],
        [0, 2, 5, 11, 10],
    ];

    #[rustfmt::skip]
    pub const EDGE_NODE_IDS_INWARD: [[usize; Tri15::EDGE_NNODE]; Tri15::NEDGE] = [
        [0, 1, 3,  6,  7],
        [1, 2, 4,  8,  9],
        [2, 0, 5, 10, 11],
    ];

    #[rustfmt::skip]
    pub const NODE_REFERENCE_COORDS: [[f64; Tri15::GEO_NDIM]; Tri15::NNODE] = [
        [0.0  , 0.0 ], //  0
        [1.0  , 0.0 ], //  1
        [0.0  , 1.0 ], //  2
        [0.5  , 0.0 ], //  3
        [0.5  , 0.5 ], //  4
        [0.0  , 0.5 ], //  5
        [0.25 , 0.0 ], //  6
        [0.75 , 0.0 ], //  7
        [0.75 , 0.25], //  8
        [0.25 , 0.75], //  9
        [0.0  , 0.75], // 10
        [0.0  , 0.25], // 11
        [0.25 , 0.25], // 12
        [0.5  , 0.25], // 13
        [0.25 , 0.5 ], // 14
    ];

    pub const INTERIOR_NODES: [usize; Tri15::N_INTERIOR_NODE] = [12, 13, 14];

    #[rustfmt::skip]
    pub const TRIANGULATE_TRIANGLES: [[usize; 3]; Tri15::TRIANGULATE_NTRIANGLE] = [
        [ 0,  6, 11],  //  0
        [ 6, 12, 11],  //  1
        [ 6,  3, 12],  //  2
        [ 3, 13, 12],  //  3
        [ 3,  7, 13],  //  4
        [ 7,  8, 13],  //  5
        [ 7,  1,  8],  //  6
        [11, 12,  5],  //  7
        [12, 14,  5],  //  8
        [12, 13, 14],  //  9
        [13,  4, 14],  // 10
        [13,  8,  4],  // 11
        [ 5, 14, 10],  // 12
        [14,  9, 10],  // 13
        [14,  4,  9],  // 14
        [10,  9,  2],  // 15
    ];

    /// Computes the interpolation functions
    ///
    /// # Output
    ///
    /// * `interp` -- interpolation function evaluated at ksi (nnode)
    ///
    /// # Input
    ///
    /// * `ksi` -- reference coordinates with length ≥ geo_ndim
    pub fn calc_interp(interp: &mut Vector, ksi: &[f64]) {
        let (r, s) = (ksi[0], ksi[1]);

        let pt1 = 128.0 / 3.0;
        let pt2 = 32.0 / 3.0;
        let cc = 1.0 - r - s;
        let t1 = r - 0.25;
        let t2 = r - 0.5;
        let t3 = r - 0.75;
        let t4 = s - 0.25;
        let t5 = s - 0.5;
        let t6 = s - 0.75;
        let t7 = cc - 0.25;
        let t8 = cc - 0.5;
        let t9 = cc - 0.75;

        interp[0] = pt2 * cc * t7 * t8 * t9;
        interp[1] = pt2 * r * t1 * t2 * t3;
        interp[2] = pt2 * s * t4 * t5 * t6;
        interp[3] = 64.0 * cc * r * t1 * t7;
        interp[4] = 64.0 * r * s * t1 * t4;
        interp[5] = 64.0 * s * cc * t4 * t7;
        interp[6] = pt1 * cc * r * t7 * t8;
        interp[7] = pt1 * cc * r * t1 * t2;
        interp[8] = pt1 * r * s * t1 * t2;
        interp[9] = pt1 * r * s * t4 * t5;
        interp[10] = pt1 * s * cc * t4 * t5;
        interp[11] = pt1 * s * cc * t7 * t8;
        interp[12] = 128.0 * r * s * cc * t7;
        interp[13] = 128.0 * r * s * t1 * cc;
        interp[14] = 128.0 * r * s * cc * t4;
    }

    /// Computes the derivatives of interpolation functions with respect to the reference coordinates
    ///
    /// # Output
    ///
    /// * `deriv` -- derivatives of the interpolation function with respect to
    ///   the reference coordinates ksi, evaluated at ksi (nnode,geo_ndim)
    ///
    /// # Input
    ///
    /// * `ksi` -- reference coordinates with length ≥ geo_ndim
    pub fn calc_deriv(deriv: &mut Matrix, ksi: &[f64]) {
        let (r, s) = (ksi[0], ksi[1]);

        let pt1 = 128.0 / 3.0;
        let pt2 = 32.0 / 3.0;
        let cc = 1.0 - r - s;
        let t1 = r - 0.25;
        let t2 = r - 0.5;
        let t3 = r - 0.75;
        let t4 = s - 0.25;
        let t5 = s - 0.5;
        let t6 = s - 0.75;
        let t7 = cc - 0.25;
        let t8 = cc - 0.5;
        let t9 = cc - 0.75;

        deriv.set(0, 0, -pt2 * (t8 * t9 * (t7 + cc) + cc * t7 * (t8 + t9)));
        deriv.set(1, 0, pt2 * (t2 * t3 * (t1 + r) + r * t1 * (t3 + t2)));
        deriv.set(2, 0, 0.0);
        deriv.set(3, 0, 64.0 * (cc * t7 * (t1 + r) - r * t1 * (t7 + cc)));
        deriv.set(4, 0, 64.0 * s * t4 * (t1 + r));
        deriv.set(5, 0, -64.0 * s * t4 * (t7 + cc));
        deriv.set(6, 0, pt1 * (cc * t7 * t8 - r * (t8 * (t7 + cc) + cc * t7)));
        deriv.set(7, 0, pt1 * (cc * (t2 * (t1 + r) + r * t1) - r * t1 * t2));
        deriv.set(8, 0, pt1 * s * (t2 * (t1 + r) + r * t1));
        deriv.set(9, 0, pt1 * s * t4 * t5);
        deriv.set(10, 0, -pt1 * s * t4 * t5);
        deriv.set(11, 0, -pt1 * s * (t8 * (t7 + cc) + cc * t7));
        deriv.set(12, 0, 128.0 * s * (cc * t7 - r * (t7 + cc)));
        deriv.set(13, 0, 128.0 * s * (cc * (t1 + r) - r * t1));
        deriv.set(14, 0, 128.0 * s * t4 * (cc - r));

        deriv.set(0, 1, -pt2 * (t8 * t9 * (t7 + cc) + cc * t7 * (t8 + t9)));
        deriv.set(1, 1, 0.0);
        deriv.set(2, 1, pt2 * (t5 * t6 * (t4 + s) + s * t4 * (t6 + t5)));
        deriv.set(3, 1, -64.0 * r * t1 * (t7 + cc));
        deriv.set(4, 1, 64.0 * r * t1 * (t4 + s));
        deriv.set(5, 1, 64.0 * (cc * t7 * (t4 + s) - s * t4 * (t7 + cc)));
        deriv.set(6, 1, -pt1 * r * (t8 * (t7 + cc) + cc * t7));
        deriv.set(7, 1, -pt1 * r * t1 * t2);
        deriv.set(8, 1, pt1 * r * t1 * t2);
        deriv.set(9, 1, pt1 * r * (t5 * (t4 + s) + s * t4));
        deriv.set(10, 1, pt1 * ((cc * (t5 * (t4 + s) + s * t4)) - s * t4 * t5));
        deriv.set(11, 1, pt1 * (cc * t7 * t8 - s * (t8 * (t7 + cc) + cc * t7)));
        deriv.set(12, 1, 128.0 * r * (cc * t7 - s * (cc + t7)));
        deriv.set(13, 1, 128.0 * r * t1 * (cc - s));
        deriv.set(14, 1, 128.0 * r * (cc * (t4 + s) - s * t4));
    }
}