Tie two non-matching meshes¶

Join two separately-meshed parts across a shared interface without remeshing them conformally. Reach for this when two members meet at a face or a point but their nodes don't line up.

Two recipes, picked by what the interface looks like:

g.constraints.tie — non-conformal surfaces. Each slave node is projected onto the closest master face and its DOFs are interpolated from that face's shape functions (u_slave = Σ Nᵢ · u_masterᵢ). The meshes do not need matching nodes.
g.constraints.equal_dof — co-located nodes. The resolver finds master/slave node pairs whose coordinates match within tolerance and ties the selected DOFs (u_slave[i] = u_master[i]). Use this when the two parts genuinely share node positions at the boundary.

Both are declared pre-mesh against physical-group / part names, resolved at get_fem_data, and auto-emitted by the typed bridge (ADR 0022) — you never hand-write ops.equalDOF or the ASDEmbeddedNodeElement penalty elements.

Recipe¶

from apeGmsh import apeGmsh
from apeGmsh.opensees import apeSees

g = apeGmsh(model_name="tie_demo")
g.begin()
# ... build two parts that meet at an interface, mesh them ...

# --- Non-matching surfaces: interpolate slave DOFs from the master face
g.constraints.tie(
    "flange_surface",   # master part/PG label
    "web_surface",      # slave part/PG label
    tolerance=1.0,      # max projection distance slave -> master face
)

# --- OR: co-located nodes -> tie the matching pairs directly
g.constraints.equal_dof(
    "beam_a_end",
    "beam_b_end",
    dofs=[1, 2, 3],     # 1-based; couple translations only
    tolerance=1e-6,
)

# Resolve: definitions become concrete node-level records on the broker
fem = g.mesh.queries.get_fem_data(dim=3)

# Build OpenSees through the typed bridge. The tie auto-emits here --
# nothing else to declare for it.
ops = apeSees(fem)
# ... ops.section / ops.element / ops.fix / ops.mass / loads ...
ops.run(...)

Order-mismatched interfaces: `method="mortar"`¶

The default tie is a collocation: each slave node is pinned to the master's interpolated field at one projected point. That is exact for matched interpolation orders, but across an order mismatch — hex20 faces tied onto hex8 faces — it over-constrains the quadratic side: the slave's midside nodes are forced onto a bilinear field, so the surface cannot deform quadratically. Measured on a solid steel fuse, that stiffened the rib-root fixity by enough to move the device stiffness +7.7 % against a conformal reference.

The fix is the integral-mortar tie:

g.constraints.tie("plate_face", "rib_face",
                  method="mortar", enforce="equation", dofs=[1, 2, 3])

method="mortar" integrates the bond over the facet overlaps with a dual (biorthogonal) slave basis instead of collocating nodes, so neither side's interpolation order is imposed on the other — and it is master/slave symmetric in a way collocation is not. It works on composed assemblies (from_h5 + compose, or Assembly with kind="tie" and method="mortar" in the couple), which is exactly where order-mismatched models live, since set_order is global per gmsh session. Requirements and limits (ADR 0086): enforce="equation" (so it needs the Lagrange handler and an unsymmetric solver, like any equation tie — and, for the live run, a Ladruno fork build; see Backend capabilities); a flat, coincident interface (tolerance is the out-of-plane gap allowance); convex facets with straight edges (every midside node at its edge midpoint — the kernel integrates on the corner polygon, which only equals the curved facet for straight edges); no master facet overlapping another (the coverage check counts multiplicity, so two layers of master surface can hide an untied slave strip); tri6 slave facets are refused (swap the sides — tri6 is fine as master). Every degenerate case is a hard MortarTieError; a mortar tie never silently resolves to nothing.

Notes / gotchas¶

Target names, never raw tags. Both factories take part / PG labels so the constraint survives a remesh — don't pass node or entity tags.
tie vs equal_dof. If the meshes share nodes, equal_dof is cheaper and exact. If they don't, equal_dof finds no pairs — use tie. For large or doubly non-matching interfaces, escalate to g.constraints.tied_contact (bidirectional projection).
DOFs are 1-based (1=ux, 2=uy, 3=uz, 4=rx, 5=ry, 6=rz). On a 3-DOF solid model only 1–3 exist; omit dofs to tie all available.
Don't re-emit it. The bridge auto-emits MP constraints from the snapshot (ADR 0022). Adding a matching raw ops.equalDOF / ops.rigidLink on top double-constrains the interface.
Tune tolerance. Too tight and no pairs/projections are found; too loose and you couple nodes that shouldn't be. equal_dof defaults to 1e-6 (geometric match); tie defaults to 1.0 (projection gap).

Tie two non-matching meshes¶

Recipe¶

Order-mismatched interfaces: method="mortar"¶

Notes / gotchas¶

See also¶

Order-mismatched interfaces: `method="mortar"`¶