Pith Number

pith:X75ZSWFA

pith:2026:X75ZSWFAVON2TVVQFKX75R6F3L

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Mixed Finite Elements for Geometrically Exact Beams using Discontinuous Rotations and Discrete Curvature

Alexander Humer, Astrid Pechstein, Ivo Steinbrecher

A mixed finite-element formulation for geometrically exact beams treats moments as independent variables to allow discontinuous rotations per element.

arxiv:2605.04573 v2 · 2026-05-06 · math.NA · cs.NA

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Claims

C1strongest claim

We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous approximation of rotations, which is key to a simple and efficient discretization framework.

C2weakest assumption

For linear constitutive laws, the mixed form is derived via a Legendre transform of the curvature-related strain energy; the assumption that this transform yields a stable and consistent discrete system for the full range of slenderness ratios and element orders.

C3one line summary

A mixed finite-element method for Simo-Reissner beams introduces the moment as an independent field and uses discrete curvature to enable discontinuous rotations while preserving objectivity and path-independence.

Receipt and verification

First computed	2026-05-20T00:06:36.403762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bffb9958a0ab9ba9d6b02aaffec7c5dadee2098a4979947519e0f6fbaa09ef2a

Aliases

arxiv: 2605.04573 · arxiv_version: 2605.04573v2 · doi: 10.48550/arxiv.2605.04573 · pith_short_12: X75ZSWFAVON2 · pith_short_16: X75ZSWFAVON2TVVQ · pith_short_8: X75ZSWFA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/X75ZSWFAVON2TVVQFKX75R6F3L \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: bffb9958a0ab9ba9d6b02aaffec7c5dadee2098a4979947519e0f6fbaa09ef2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df75075b2e49e4f6ade127fa3b94f9c4a356b4150e859481278405a5ead538e8",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-06T07:22:54Z",
    "title_canon_sha256": "8a0296babf92a20cd3d80cfe45c657272bad5a4d165f21fdfbe20c649d3b9e63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04573",
    "kind": "arxiv",
    "version": 2
  }
}