Element kernels

femorph-solver ships a structural element library. Each kernel is independently implemented from the open literature; every non-trivial algorithm (shape function, integration rule, formulation variant) carries a References block in its source module. The pre-processing pages under Element library are the user-facing how-to; this section is the engineering reference — topology, shape functions, integration rules, and cites for every element.

Solid kernels

• HEX8 — 8-node trilinear hexahedron
• HEX20 — 20-node serendipity hexahedron
• TET10 — 10-node quadratic tetrahedron
• WEDGE15 / PYR13 — degenerate-corner serendipity hex

2D & shell kernels

• QUAD4_PLANE — 4-node bilinear plane quad
• QUAD4_SHELL — 4-node Mindlin-Reissner flat shell

Line / point kernels

• BEAM2 — 3D 2-node Euler-Bernoulli beam
• TRUSS2 — 2-node 3D axial bar
• SPRING — 2-node longitudinal spring
• POINT_MASS — single-node lumped translational mass

Reference-element topology

Each kernel works on a canonical parametric reference element. These figures show the local node numbering used by femorph-solver internally; downstream assembly maps the parametric coordinates \((\xi, \eta, \zeta)\) to physical space through the element’s Jacobian.

HEX8 — 8 corner nodes on the bi-unit cube.

TET10 — 4 corners + 6 mid-edges in the unit tetrahedron.

QUAD4 — 4 corners on the bi-unit square.

BEAM2 — 2 endpoints, 6 DOFs each (3 translations + 3 rotations).

HEX20 inherits HEX8’s corner numbering and adds 12 mid-edge nodes 9-20 in the standard MAPDL SOLID186 order (bottom-face mid-edges, top-face mid-edges, vertical mid-edges). See HEX20 — 20-node serendipity hexahedron for the full per-element page.

Quick reference table

Kernel	DOFs / node	Stiffness rule	Mass rule
HEX8 — 8-node trilinear hexahedron	3	2 × 2 × 2 Gauss + B-bar / EAS	2 × 2 × 2 Gauss
HEX20 — 20-node serendipity hexahedron	3	2 × 2 × 2 reduced (Bedrosian)	14-pt Irons
TET10 — 10-node quadratic tetrahedron	3	4-pt Keast	4-pt Keast
WEDGE15 / PYR13 — degenerate-corner serendipity hex	3	Dunavant × Gauss / Duffy	Dunavant × Gauss / Duffy
QUAD4_PLANE — 4-node bilinear plane quad	2	2 × 2 Gauss	2 × 2 Gauss
QUAD4_SHELL — 4-node Mindlin-Reissner flat shell	6	2 × 2 + 1 × 1 SR shear	2 × 2 Gauss
BEAM2 — 3D 2-node Euler-Bernoulli beam	6	Closed-form Hermite cubic	Closed-form (consistent / lumped)
TRUSS2 — 2-node 3D axial bar	3	Closed-form linear	Closed-form (consistent / lumped)
SPRING — 2-node longitudinal spring	3	Closed-form 1×1	—
POINT_MASS — single-node lumped translational mass	3	—	Diagonal lumped 3×3

See also

Element library — per-element integration flags, material-property slots, and runnable demos.