{
  "abstract": "Checkerboard edge-midpoint geometry provides an exact planar Varignon parallelogram for every spatial quadrilateral, allowing a local tangent frame and normal to be recovered directly from nodal positions even when the raw quadrilateral is warped. Building on this property, we develop a position-only thin-shell discretization with no independent director, rotation, or strain variables. The connected edge-midpoint surface is taken as the physical midsurface: the first fundamental form is evaluated on planar B faces, while a W-centered second fundamental form is constructed from variations of neighboring B-face normals, so membrane and bending share the same geometric carrier. A variational-kernel analysis shows that smooth second-order consistency does not eliminate lattice-scale blind modes. After quotienting out the raw checkerboard gauge, the B metric has one physical membrane blind direction and the symmetric W curvature has two curvature blind directions. We introduce a quotient-minimal membrane compatibility coordinate $X_M$ and an objective reference-relative curvature coordinate $X_W^{rel}$, placed consistently in the $O(t)$ membrane and $O(t^3)$ bending sectors. The formulation admits an explicit midpoint quotient, complete flat blind-mode classification, rigid-motion objectivity, reference-state consistency, and an $O(h^2)$ near-isometry approximation result for aligned generalized cylinders. Numerical tests show second-order curvature convergence, targeted removal of the membrane defect, and a sub-percent, refinement-decaying influence of $X_W^{rel}$. Linear and nonlinear shell benchmarks further demonstrate flat bending, curved-shell membrane-bending coupling, thickness sensitivity, large rotation, nonlinear pinching, and localized ovalization within a single position-only framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30195",
  "author_total": 8,
  "authors": [
    {
      "name": "Junjie Song"
    },
    {
      "name": "Xuanyu Wu"
    },
    {
      "name": "Zhifeng Zhang"
    },
    {
      "name": "Bingtao Hu"
    },
    {
      "name": "Zhaoxi Hong"
    },
    {
      "name": "Xiuju Song"
    },
    {
      "name": "Yixiong Feng"
    },
    {
      "name": "Jianrong Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1rm4ynxvpwm3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30195",
  "fulltext_url": null,
  "id": "f1rm4ynxvpwm3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30195",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7204907076",
  "pdf_url": "https://arxiv.org/pdf/2608.30195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1rm4ynxvpwm3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Checkerboard Shells: A Position-Only Thin-Shell Discretization with Scale-Compatible Completion",
  "title_text": "Checkerboard Shells: A Position-Only Thin-Shell Discretization with Scale-Compatible Completion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/f1rm4ynxvpwm3",
  "venue": "arXiv",
  "versions": []
}