88 lines
2.9 KiB
Python
88 lines
2.9 KiB
Python
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"""Modal analysis verification.
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A 1-DOF lumped-mass cantilever pole. The fundamental natural frequency
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of the lateral mode is ω = √(k/m), where k = 3EI/L³ for a tip-mass
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cantilever flexural spring.
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The runner auto-falls back to ``-fullGenLapack`` for small models —
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ARPACK can't allocate enough Arnoldi workspace when the active DOF
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count is tiny, which is exactly the SDOF case.
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"""
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from __future__ import annotations
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import math
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import pytest
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ops = pytest.importorskip("openseespy.opensees") # noqa: F401
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from otko.core import ( # noqa: E402
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ElasticBeamColumn,
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ElasticSection,
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ModalCase,
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Node,
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Project,
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)
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from otko.services import OpenSeesRunner # noqa: E402
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def test_sdof_pole_first_frequency_matches_kspring_over_m() -> None:
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"""Vertical pole, mass at top, fixed base. ω₁ = √(3EI/(mL³))."""
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L = 3.0
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E = 200e9
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A = 0.01
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I = 8.333e-6
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m_tip = 1000.0
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project = Project(
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ndm=2, ndf=3,
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nodes=[
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Node(id=1, coords=(0.0, 0.0, 0.0), restraint=(True, True, False, False, False, True)),
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Node(id=2, coords=(0.0, L, 0.0),
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mass=(m_tip, m_tip, 0.0, 0.0, 0.0, 0.0)),
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],
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sections=[ElasticSection(id=1, E=E, A=A, Iz=I)],
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elements=[ElasticBeamColumn(id=1, nodes=(1, 2), section_id=1)],
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)
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case = ModalCase(id=1, name="SDOF-Pole", n_modes=1)
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results = OpenSeesRunner(project).run(case)
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# Lateral cantilever spring stiffness:
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k = 3.0 * E * I / L**3
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omega_expected = math.sqrt(k / m_tip)
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omega_actual = float(results.angular_frequencies[0])
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assert math.isclose(omega_actual, omega_expected, rel_tol=5e-3), (
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f"ω₁ mismatch: expected {omega_expected:.4f} rad/s, got {omega_actual:.4f} rad/s"
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)
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def test_runner_falls_back_to_lapack_for_small_models() -> None:
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"""Verify the fallback rule: small n_free triggers Lapack instead of ARPACK."""
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from unittest.mock import MagicMock
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project = Project(
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ndm=2, ndf=3,
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nodes=[
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Node(id=1, coords=(0.0, 0.0, 0.0), restraint=(True, True, False, False, False, True)),
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Node(id=2, coords=(0.0, 3.0, 0.0),
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mass=(1000.0, 1000.0, 0.0, 0.0, 0.0, 0.0)),
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],
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sections=[ElasticSection(id=1, E=200e9, A=0.01, Iz=8.333e-6)],
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elements=[ElasticBeamColumn(id=1, nodes=(1, 2), section_id=1)],
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)
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mock_ops = MagicMock()
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mock_ops.eigen.return_value = [1.0]
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mock_ops.nodeEigenvector.return_value = 0.0
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runner = OpenSeesRunner(project, ops_module=mock_ops)
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runner.run(ModalCase(id=1, name="t", n_modes=1)) # default solver = 'genBandArpack'
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# n_free = (3 - 2) + (3 - 1) = 3, and 2 * n_modes = 2 >= n_free? No, 2 < 3.
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# Adjust: ask for 2 modes — 2*2 = 4 >= 3 → must trigger fallback.
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mock_ops.reset_mock()
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mock_ops.eigen.return_value = [1.0, 4.0]
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runner.run(ModalCase(id=2, name="t2", n_modes=2))
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mock_ops.eigen.assert_called_with("-fullGenLapack", 2)
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