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Warped CQUAD4 rigid again: BMEAN in the element axes (MIN4/MIN4T), K6ROT on warped shells - #322
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…ement axes it is used in CALC_BMEANT builds BMEAN from the geometry in the axes with x along side 1-2 (X12...Y4 from QUAD_GEOM_CHECK, TE_12), but with the default QUADAXIS = 'SPLITD' the membrane matrices it multiplies (QMEM1 KE, PTE, BIG_BM) are in the final axes TE = CT_QD*TE_12. For a warped quad with QUAD_DELTA /= 0 the stiffness was then not rigid: a rigid rotation about an in-plane axis gave grid forces in proportion to HBAR (PARAM,EQCHECK), and free-free models with warped quads lost rigid modes. Each 3x2 block of BMEAN is now rotated by CT_QD. Present in release 19; MITC4/MITC4+ and QUADAXIS = 'SIDE12' were never affected. Checks (EQCHECK, rigid-rotation grid forces): a single warped quad (HBAR 0.04 on 13 x 16) 1.24E+03 before, 1.0 after (the flat element's level), unchanged at 10x the warp. A 852-grid shell airframe, free-free: 9 zero modes and three rigid rotations at 4.6, 6.9 and 11.7 Hz before; 12 zero modes after, first elastic mode 531 Hz (534 Hz with SIDE12). Test (MYSTRAN_Validation): warped_quad4_rigid_rotation_min4.bdf, a warped unsymmetric quad with grids 1-3 held at a small rigid rotation; grid 4 must follow it. Current dev misses by up to 4.5%.
CALC_K6ROT measures the rotation of each edge about the element normal n from the translations of its end nodes, (n x d).(u_next - u_n) / (2|d|^2), and compares it with n . r_n. When an edge d is not in the element plane (a warped MITC4 quad, whose XEL has z coordinates, or a warped MIN4/MIN4T quad, whose grids are -HBAR, +HBAR, -HBAR, +HBAR from the mean plane XEL lies in), a rigid rotation w about an in-plane axis gives edge terms of (n.d)(w.d) / (2|d|^2) that n . r_n does not cancel, so the spring resisted rigid rotation. The rotation of node n now enters as n - sum over its 2 edges of (n.d) d / (2|d|^2), which makes the spring strain zero for every rigid motion and is n alone when the edges lie in the plane (flat elements unchanged). For MIN4/MIN4T the edge vectors now include the grids' heights from the mean plane. Checks: - PARAM,EQCHECK (rigid-rotation grid forces) on a warped quad with K6ROT 100: at the flat element's level for MIN4, MIN4T and MITC4 at 1x and 10x the warp. - A 852-grid shell airframe, free-free, K6ROT 100: rigid rotations at 0.30, 0.46 and 0.71 Hz before (after the BMEAN fix), 12 zero modes after (first elastic mode 532 Hz MIN4, 604 Hz MITC4). Tests (MYSTRAN_Validation): warped_quad4_rigid_rotation_k6rot.bdf (MITC4 + K6ROT 100), a warped quad with grids 1-3 held at a small rigid rotation; grid 4 must follow it (current dev misses by up to 0.4%, R3 5.7E-5 where it is 0). The bulk reference of "hemisphere with cutout 4e-4 mitc4+ SNORM K6ROT" is regenerated: its results move toward the same deck without K6ROT and toward the benchmark (load point 0.091269 before, 0.091304 after, 0.091304 without K6ROT, reference 0.091428); its individual-value checks are unchanged.
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Fixes #321.
Two commits, one per defect.
ELEMENT_GEOMETRY_PREPARATION.f03.SHELL_ROTATION_SUPPORT.f03.Checks:
PARAM,EQCHECK,0,1rigid-rotation grid forces on a warped quad drop to the flat-element level for MIN4, MIN4T and MITC4, with and without K6ROT, at 1x and 10x the warp.Tests: MYSTRAN_Validation MystranSolver/MYSTRAN_Validation#37.
warped_quad4_rigid_rotation_min4.bdfandwarped_quad4_rigid_rotation_k6rot.bdf(MITC4 + K6ROT): a warped unsymmetric quad with grids 1-3 held at a small rigid rotation. Grid 4 must follow it (11 checks).devall 11 fail.Validation suite: with both PRs, 1 failure of 3,266 checks, the same one current
devhas without them ("mitc4 thermal strain free rectangle cylinder"). The 11 new checks and the regenerated hemisphere pass.