LE2: Bending a cylindrical shell patch

Status: passed

Linear elasticity / LE2

Scope

Check curved-shell bending under a distributed edge couple.

Geometry

Cylindrical patch: radius 1 m, axial width 0.5 m, angle 10 degrees, thickness 0.01 m. E lies at angle 20/3 degrees and axial coordinate 0.3 m.

Material

Isotropic elastic E=210 GPa, Poisson ratio 0.3.

Boundary conditions and loading

Clamp the zero-angle edge; suppress axial displacement on both axial-width boundaries. Apply 1000 N m per metre about the cylinder axis on the opposite edge.

Assumptions

Static infinitesimal-strain bending, no pressure or thermal strain.

AM-DT formulation

AM-DT S4 shells on successively refined regular body-fitted grids; the 10 degree physical patch and interior sampling location match the fine source model. The production section operator supplies membrane and curvature strains from the assembled displacement solution.

Measurement location and recovery

Extrapolate surface quadrature strains to E, evaluate at positive half-thickness, form the global plane-stress tensor and project along the circumferential tangent. Do not use thickness-averaged stresses.

Acceptance policy

Predeclared AM-DT policy: 2% agreement with the published bending stress and 2% refinement change; not a NAFEMS certification threshold.

Original schematic of the benchmark geometry and loading
Original AM-DT schematic; dimensions and loading follow the cited specification.

Reference observables

outerTangentialStressAtE_Pa = 6e+07 Pa

AM-DT solver results

outerTangentialStressAtE_Pa

ElementsDOFsAM-DT valueReference
12085860057451.9 Pa60000000
480315060179964.4 Pa60000000

Normalized error: 0.2999%; refinement change: 0.2042%.

Run UTC: 2026-10-07T02:25:59.212438+00:00; wall time: 2.65 s.

Reproducibility: revisions and artifact hashes
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    "libdtConstantsServer.so": "8f9f9ba6dfee5f46be83995f442fc51ec94b01c1c3d08fdedad4e39a26a1e057",
    "libdtCrystalPlasticity.so": "6130b4e7c59129b4e8bd37ae445f0c6e73c6fd6e255a52662d71eb8f8a9a9e8f",
    "libdtFiniteElementMethod.so": "f595989347e56b55925e0d6bae52406d4756392392a816dcc951af01f727af50",
    "libdtLITRISOL.so": "202a10e6de1058a033ebeb7a1febbdf73002c24bc75493e38b2b0fb668ff9aaa",
    "libdtMechanicalSolver.so": "6e574945666c4e1df2b5c9b8b37ab089c3414ffb3e8bc94e325380d851798d33",
    "libdtPartScaleMechanicalServer.so": "5a2ea08c7eff48703eec23fc1584f860aebf7ffe722e0951a74e33888f851ae6",
    "libdtPartScaleThermalServer.so": "bca1dcad80e389f5df3e250803771d7630d6b0405997c6b77036ef2bc9f29050",
    "libdtScanPathGeneratorServer.so": "fef36783aebc2f5f4edb3358e727524ecb9cc41f1cdd76b326467a6ba0eeb91f",
    "libpython3.11.so.1.0": "f72bbb1a96cb12d3f39d0a7acd58320b5bf8681d4d26bfc05f43edb4a1cfdc66",
    "libpython3.9.so.1.0": "f10e20c9adbff54099aa873247183816d9250e35fb3100b58766d15493ba7a35"
  }
}

Source: NAFEMS LE2 in the Abaqus benchmark manual.