forked from 1b-agent/fieldcraft-upstream
fem: pyramid5 element (solver, quality, decks, VTK)
A five-node pyramid, the conforming transition between a hexahedron's face and tetrahedra: Bedrosian's rational shape functions with a collapsed (Duffy) Gauss rule, a certified Jacobian on the base square with exact volume, a scaled Jacobian, C3D5 / CPYRAM / LS-DYNA degenerate solid, VTK_PYRAMID and the binary mesh code 13. A distorted hex8-pyramid5-tet4 transition mesh passes the patch test and uniaxial tension exactly. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed
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@@ -17,6 +17,7 @@ pub struct Node {
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/// - rod3: the two ends, then the middle node;
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/// - tet10: mid-side nodes 5–10 on edges 1-2, 2-3, 3-1, 1-4, 2-4, 3-4;
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/// - wedge6: triangle 1-2-3, then 4-5-6 on the side its right-hand normal points to;
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/// - pyramid5: base 1-2-3-4, then the apex 5 on the side its right-hand normal points to;
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/// - hex8/hex20: face 1-2-3-4, then 5-6-7-8 above it; hex20's mid-side nodes 9–12 lie on the
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/// edges of 1-2-3-4, 13–16 on those of 5-6-7-8, and 17–20 on edges 1-5, 2-6, 3-7, 4-8.
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///
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@@ -47,6 +48,9 @@ pub enum ElementKind {
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Tet10,
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/// Six-node wedge (pentahedron).
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Wedge6,
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/// Five-node pyramid: a quadrilateral base and an apex; the transition between a hexahedron's
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/// face and tetrahedra.
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Pyramid5,
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/// Eight-node hexahedron.
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Hex8,
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/// Twenty-node hexahedron.
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@@ -54,7 +58,7 @@ pub enum ElementKind {
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}
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impl ElementKind {
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pub const ALL: [ElementKind; 12] = [
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pub const ALL: [ElementKind; 13] = [
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ElementKind::Rod2,
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ElementKind::Rod3,
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ElementKind::Beam2,
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@@ -65,6 +69,7 @@ impl ElementKind {
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ElementKind::Tet4,
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ElementKind::Tet10,
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ElementKind::Wedge6,
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ElementKind::Pyramid5,
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ElementKind::Hex8,
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ElementKind::Hex20,
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];
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@@ -74,6 +79,7 @@ impl ElementKind {
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ElementKind::Rod2 | ElementKind::Beam2 => 2,
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ElementKind::Rod3 | ElementKind::Tri3 => 3,
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ElementKind::Quad4 | ElementKind::Tet4 => 4,
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ElementKind::Pyramid5 => 5,
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ElementKind::Tri6 | ElementKind::Wedge6 => 6,
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ElementKind::Quad8 | ElementKind::Hex8 => 8,
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ElementKind::Tet10 => 10,
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@@ -87,6 +93,7 @@ impl ElementKind {
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ElementKind::Rod2 | ElementKind::Rod3 | ElementKind::Beam2 => 2,
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ElementKind::Tri3 | ElementKind::Tri6 => 3,
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ElementKind::Quad4 | ElementKind::Quad8 | ElementKind::Tet4 | ElementKind::Tet10 => 4,
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ElementKind::Pyramid5 => 5,
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ElementKind::Wedge6 => 6,
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ElementKind::Hex8 | ElementKind::Hex20 => 8,
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}
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@@ -102,7 +109,7 @@ impl ElementKind {
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match self {
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ElementKind::Rod2 | ElementKind::Rod3 | ElementKind::Beam2 => 1,
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ElementKind::Tri3 | ElementKind::Tri6 | ElementKind::Quad4 | ElementKind::Quad8 => 2,
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ElementKind::Tet4 | ElementKind::Tet10 | ElementKind::Wedge6 | ElementKind::Hex8 | ElementKind::Hex20 => 3,
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ElementKind::Tet4 | ElementKind::Tet10 | ElementKind::Wedge6 | ElementKind::Pyramid5 | ElementKind::Hex8 | ElementKind::Hex20 => 3,
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}
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}
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@@ -119,6 +126,7 @@ impl ElementKind {
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ElementKind::Tet4 => "tet4",
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ElementKind::Tet10 => "tet10",
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ElementKind::Wedge6 => "wedge6",
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ElementKind::Pyramid5 => "pyramid5",
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ElementKind::Hex8 => "hex8",
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ElementKind::Hex20 => "hex20",
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}
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@@ -135,7 +143,8 @@ impl ElementKind {
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/// normal points out of the element. Hexahedra: 1 is the face of nodes 1-2-3-4, 2 the face
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/// of 5-6-7-8, then the four sides along edges 1-2, 2-3, 3-4 and 4-1. Tetrahedra: 1 is
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/// 1-2-3, then the faces opposite node 3, node 1 and node 2. Wedges: the two triangles, then
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/// the sides along edges 1-2, 2-3 and 3-1.
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/// the sides along edges 1-2, 2-3 and 3-1. Pyramids: 1 is the base 1-2-3-4, then the
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/// triangles on edges 1-2, 2-3, 3-4 and 4-1 with the apex 5.
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/// - Shells: face 1 is the side the element's right-hand normal points to, face 2 the other.
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/// - Line elements have none.
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pub fn faces(self) -> &'static [&'static [usize]] {
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@@ -148,6 +157,7 @@ impl ElementKind {
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ElementKind::Tet4 => &[&[0, 2, 1], &[0, 1, 3], &[1, 2, 3], &[0, 3, 2]],
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ElementKind::Tet10 => &[&[0, 2, 1, 6, 5, 4], &[0, 1, 3, 4, 8, 7], &[1, 2, 3, 5, 9, 8], &[0, 3, 2, 7, 9, 6]],
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ElementKind::Wedge6 => &[&[0, 2, 1], &[3, 4, 5], &[0, 1, 4, 3], &[1, 2, 5, 4], &[2, 0, 3, 5]],
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ElementKind::Pyramid5 => &[&[0, 3, 2, 1], &[0, 1, 4], &[1, 2, 4], &[2, 3, 4], &[3, 0, 4]],
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ElementKind::Hex8 => &[&[0, 3, 2, 1], &[4, 5, 6, 7], &[0, 1, 5, 4], &[1, 2, 6, 5], &[2, 3, 7, 6], &[3, 0, 4, 7]],
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ElementKind::Hex20 => &[
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&[0, 3, 2, 1, 11, 10, 9, 8],
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@@ -174,6 +184,7 @@ impl ElementKind {
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ElementKind::Tet4 => &[&[0, 1], &[1, 2], &[2, 0], &[0, 3], &[1, 3], &[2, 3]],
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ElementKind::Tet10 => &[&[0, 1, 4], &[1, 2, 5], &[2, 0, 6], &[0, 3, 7], &[1, 3, 8], &[2, 3, 9]],
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ElementKind::Wedge6 => &[&[0, 1], &[1, 2], &[2, 0], &[3, 4], &[4, 5], &[5, 3], &[0, 3], &[1, 4], &[2, 5]],
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ElementKind::Pyramid5 => &[&[0, 1], &[1, 2], &[2, 3], &[3, 0], &[0, 4], &[1, 4], &[2, 4], &[3, 4]],
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ElementKind::Hex8 => &[&[0, 1], &[1, 2], &[2, 3], &[3, 0], &[4, 5], &[5, 6], &[6, 7], &[7, 4], &[0, 4], &[1, 5], &[2, 6], &[3, 7]],
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ElementKind::Hex20 => &[
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&[0, 1, 8],
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@@ -539,6 +550,7 @@ mod tests {
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ElementKind::Quad4 | ElementKind::Quad8 => vec![[0., 0., 0.], [1., 0., 0.], [1., 1., 0.], [0., 1., 0.]],
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ElementKind::Tet4 | ElementKind::Tet10 => vec![[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.]],
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ElementKind::Wedge6 => vec![[0., 0., 0.], [1., 0., 0.], [0., 1., 0.], [0., 0., 1.], [1., 0., 1.], [0., 1., 1.]],
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ElementKind::Pyramid5 => vec![[0., 0., 0.], [1., 0., 0.], [1., 1., 0.], [0., 1., 0.], [0.5, 0.5, 1.]],
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ElementKind::Hex8 | ElementKind::Hex20 => {
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vec![[0., 0., 0.], [1., 0., 0.], [1., 1., 0.], [0., 1., 0.], [0., 0., 1.], [1., 0., 1.], [1., 1., 1.], [0., 1., 1.]]
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}
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@@ -589,6 +601,7 @@ mod tests {
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assert_eq!(ElementKind::Hex8.faces().len(), 6);
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assert_eq!(ElementKind::Tet4.faces().len(), 4);
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assert_eq!(ElementKind::Wedge6.faces().len(), 5);
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assert_eq!(ElementKind::Pyramid5.faces().len(), 5);
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assert_eq!(ElementKind::Hex20.edges().len(), 12);
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for kind in ElementKind::ALL {
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let mid_sides = kind.edges().iter().filter(|e| e.len() == 3).count();
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