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OneCAD-Simulation/docs/elements.md
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bd55abea7f FEM foundation A: DofKind/DofLayout, shape-function library with Hessians, solvers on DofLayout (#35)
* fem: DofKind/DofLayout and the shape-function library with second derivatives

DofKind (Ux..Rz, T, P), DofSet, ElementDofs (per-node kinds and condensed
internal unknowns) and DofLayout: mesh nodes by label, kinds in order, then
reference points. basis::Basis covers line2/3, tri3/6, quad4/8/9, tet4/10,
wedge6/15, pyramid5, hex8/20/27 with values, first and second natural
derivatives (second-order forward AD, fem::jet) and the physical gradients,
Hessians and Laplacians with the map's second-derivative term. Tested for
Kronecker delta, partition of unity, polynomial completeness, finite
differences, affine and curved maps.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* solver, explicit: number degrees of freedom with DofLayout

The implicit mesh numbers its unknowns with a DofLayout (mesh nodes by label
with the kinds their elements declare, then six per coupled reference point);
assembly adds element blocks by (node, DofKind), so a node may carry any mix
of kinds; couplings, boundary conditions, loads and results address
(node, kind). The explicit system keeps node-major translations, now checked
against its layout (NODE_DOFS). Solid formulations declare their ElementDofs.

Every static, frequency and explicit result of the solver, explicit, engine
and io test suites hashes bit-identically before and after (957 results).
docs/fem.md describes the DOF model and the shape-function conventions.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* fem, solver: simplify after review

Block offsets resolved once per node pair; add_scalar/add_diagonal take
the kinds like add_block; one checked Jacobian inverse (dense::positive_inverse)
for the solid kernels and the basis library; static natural-node tables; the
Hessian path inverts the Jacobian once.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

---------

Co-authored-by: jyviko <[email protected]>
Co-authored-by: Claude Opus 5.5 <[email protected]>
2026-10-13 19:54:32 -04:00

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Element library

ModelCraft's finite element library (crates/fem), family by family, with status. The scope is modelled on what a full CAE code offers (Abaqus's element library is the reference for breadth); names, formulations and tests are our own, written from the published literature. Deck writers map each of our elements to each solver's name (see crates/decks). Simple elements first: 1D and 2D, then shells, special-purpose and multiphysics elements.

Status: done (on main, verified against analytic solutions), in progress (an agent task is open), planned.

Every element builds on the shared foundation of docs/fem.md: it declares its nodal degrees of freedom (DofKind: translations, rotations, temperature, pressure) and condensed internal ones (ElementDofs), the solvers number them with DofLayout, and its interpolation comes from the shape-function library (Basis: line2/3, tri3/6, quad4/8/9, tet4/10, wedge6/15, pyramid5, hex8/20/27 with first and second derivatives).

Point and discrete elements

Element Use Status
Point mass Lumped mass at a node or reference point (isotropic or per direction) in progress (1D elements I)
Rotary inertia Inertia tensor at a 6-DOF node in progress (1D elements I)
Spring to ground / two-point spring Linear spring in a fixed direction or along the line of nodes in progress (1D elements I)
Dashpot to ground / two-point Linear viscous damper (dynamic steps; ignored in static) in progress (1D elements I)
Nonstructural mass Mass spread over a region without stiffness planned
Connectors Kinematic joints (hinge, slot, universal…) with elasticity, damping, stops planned (M7)

1D elements

Element Use Status
Truss, 2-node (2D and 3D) Axial members, cables (compression allowed) in progress (1D elements I)
Truss, 3-node (2D and 3D) Curved axial members in progress (1D elements I)
Beam, 2-node Timoshenko, 3D Frames, stiffeners; shear deformable in progress (shells and beams)
Beam, 2-node Euler–Bernoulli (cubic), 2D and 3D Slender frames; exact for end-loaded prismatic members planned (1D elements II)
Beam, 3-node Timoshenko (quadratic), 2D and 3D Curved and stocky beams planned (1D elements II)
Beam, 2D (planar frames) In-plane frames with 3 DOFs per node planned (1D elements II)
Pipe / elbow Pipes with internal pressure, ovalisation planned (1D elements II)
Open-section beams with warping Thin-walled sections in torsion planned
Rebar / stringers Reinforcement along edges or embedded planned

2D elements

Element Use Status
Plane stress tri3, tri6, quad4, quad8 Thin plates loaded in their plane in progress (2D elements)
Plane strain tri3, tri6, quad4, quad8 Long sections (dams, tunnels, extrusions) in progress (2D elements)
Axisymmetric tri3, tri6, quad4, quad8 Revolved solids (shafts, vessels, discs) in progress (2D elements)
Incompatible-mode and reduced-integration quads Bending-accurate and cheap variants in progress (2D elements)
Generalized plane strain Plane strain with a free out-of-plane strain planned
Axisymmetric with twist Revolved parts under torsion planned
Axisymmetric shells (2-node, 3-node) Thin revolved shells (tanks, domes) planned
Hybrid (mixed u–p) variants Nearly incompressible materials planned

Shells and membranes

Element Use Status
Shell quad4 (MITC4), triangle (locking-free) Thin and thick shells in progress (shells and beams)
Shell quad8 / tri6 Curved thick shells planned
Continuum shells (8-node, on swept hex) Thick-to-thin shells, composites through thickness planned (M8)
Membranes (tri3, quad4, quad8) Fabrics, inflatables, skins without bending planned
Surface elements Massless surfaces for loads and contact planned
Composite layups on shells Ply tables, orientations planned (M8)

3D solids

Element Use Status
tet4, tet10 Free meshes of any part done
hex8 (full, incompatible modes), hex20 (full, reduced) Structured and swept meshes done
wedge6 Swept meshes from triangles, transitions done
hex8 one-point with hourglass control, nodal-pressure tet4 (explicit) Explicit dynamics done
wedge15, pyramid5/13 Quadratic transitions, tet–hex transition planned (M5); wedge15 and pyramid5 shape functions done
Hybrid (mixed u–p) solids Nearly incompressible materials (rubber) in progress (FEM foundation, phase C); pressure DOF kind done
Modified quadratic tet (tet10 for contact/plasticity) Robust quadratic tets planned

Special-purpose and multiphysics

Element Use Status
Cohesive (2D, 3D) Adhesive layers, delamination planned
Gasket Through-thickness gasket behaviour planned
Infinite elements Unbounded domains planned
Heat transfer (all shapes), coupled temperature–displacement Thermal and thermal-stress analyses in progress (FEM foundation, phase B); temperature DOF kind done
Acoustic Fluid acoustics, structural–acoustic coupling planned
Rigid elements Rigid bodies from meshes planned (M7)