70 lines
2.1 KiB
Python
70 lines
2.1 KiB
Python
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"""Static analysis verification.
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Cantilever beam: tip lateral load → tip displacement δ = P L³ / (3 E I).
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Compares the runner's static result against the closed-form solution.
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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") # skip if OpenSeesPy not installed
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from otko.core import ( # noqa: E402
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ElasticBeamColumn,
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ElasticSection,
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LinearTimeSeries,
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NodalLoad,
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Node,
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PlainLoadPattern,
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Project,
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StaticCase,
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)
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from otko.services import OpenSeesRunner # noqa: E402
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pytestmark = pytest.mark.slow
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def test_cantilever_tip_deflection_matches_closed_form() -> None:
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"""Horizontal cantilever in 2D: P at tip, expect δ = P L³ / (3 E I)."""
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L = 5.0
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P = 1000.0
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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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project = Project(
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ndm=2,
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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=(L, 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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time_series=[LinearTimeSeries(id=1)],
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load_patterns=[
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PlainLoadPattern(
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id=1,
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time_series_id=1,
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# Fy at the tip (downward); Rz of node 1 is restrained, others free.
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nodal_loads=[NodalLoad(node_id=2, forces=(0.0, -P, 0.0, 0.0, 0.0, 0.0))],
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)
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],
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)
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case = StaticCase(id=1, name="Cantilever", pattern_ids=[1])
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results = OpenSeesRunner(project).run(case)
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delta_expected = -P * L**3 / (3.0 * E * I) # negative (downward)
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delta_actual = results.disp(node_id=2, dof=2) # Uy at node 2
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assert math.isclose(
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delta_actual, delta_expected, rel_tol=1e-3
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), f"Tip deflection mismatch: expected {delta_expected:.6e}, got {delta_actual:.6e}"
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# Reaction at the support equals the applied load.
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Fy_reaction = results.node_reaction[1][0, 1]
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assert math.isclose(Fy_reaction, P, rel_tol=1e-6)
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