| """Compare first bending mode and static deflection from STEP tetrahedra.""" |
|
|
| import argparse |
| import hashlib |
| import json |
| import math |
| import subprocess |
| import sys |
| from pathlib import Path |
|
|
| ROOT = Path(__file__).resolve().parent |
|
|
|
|
| def measure(step: Path, setup: dict) -> dict: |
| import cadquery as cq |
| import gmsh |
| from OCP.BRepGProp import BRepGProp |
| from OCP.GProp import GProp_GProps |
|
|
| shape = cq.importers.importStep(str(step)).val() |
| if shape.ShapeType() != "Solid" or not shape.isValid() or len(shape.Solids()) != 1: |
| raise ValueError(f"Expected one valid solid: {step}") |
| props = GProp_GProps() |
| BRepGProp.VolumeProperties_s(shape.wrapped, props) |
| if props.Mass() <= 0: |
| raise ValueError("Beam volume must be positive") |
| pad0 = cq.Solid.makeBox(10, 20, 10, cq.Vector(0, -10, -5)) |
| pad1 = cq.Solid.makeBox(10, 20, 10, cq.Vector(90, -10, -5)) |
| slabs = [cq.Solid.makeBox(10, 20, 20, cq.Vector(x, -10, -10)) |
| for x in (0, 90)] |
| envelope = cq.Solid.makeBox(100, 20, 12, cq.Vector(0, -10, -6)) |
| pads = (pad0, pad1) |
| pad_overlap = sum(pad.intersect(shape).Volume() for pad in pads) |
| slab_overlap = sum(slab.intersect(shape).Volume() for slab in slabs) |
| result = { |
| "step_sha256": hashlib.sha256(step.read_bytes()).hexdigest(), |
| "volume_mm3": props.Mass(), |
| "mass_kg": props.Mass() * setup["material_density_kg_m3"] * 1e-9, |
| "end_pad_missing_mm3": max(0.0, sum(p.Volume() for p in pads) - pad_overlap), |
| "end_pad_excess_mm3": max(0.0, slab_overlap - pad_overlap), |
| "envelope_excess_mm3": max(0.0, shape.Volume() - |
| shape.intersect(envelope).Volume()), |
| "meshes": {}, |
| } |
| gmsh.initialize() |
| try: |
| gmsh.option.setNumber("General.Terminal", 0) |
| gmsh.model.add("resonance_beam") |
| gmsh.model.occ.importShapes(str(step)) |
| gmsh.model.occ.synchronize() |
| if len(gmsh.model.getEntities(3)) != 1: |
| raise ValueError("STEP import must produce one volume") |
| for size in setup["mesh_sizes_mm"]: |
| gmsh.model.mesh.clear() |
| gmsh.option.setNumber("Mesh.CharacteristicLengthMin", size) |
| gmsh.option.setNumber("Mesh.CharacteristicLengthMax", size) |
| gmsh.option.setNumber("Mesh.Algorithm3D", 1) |
| gmsh.model.mesh.generate(3) |
| tags, coordinates, _ = gmsh.model.mesh.getNodes() |
| nodes = {str(int(tag)): [coordinates[3 * i + axis] / 1000 |
| for axis in range(3)] |
| for i, tag in enumerate(tags)} |
| types, _, element_nodes = gmsh.model.mesh.getElements(3) |
| tets = [] |
| for kind, connectivity in zip(types, element_nodes): |
| if kind != 4: |
| raise ValueError(f"Expected first-order tetrahedra, got {kind}") |
| tets.extend([[int(value) for value in connectivity[i:i + 4]] |
| for i in range(0, len(connectivity), 4)]) |
| if not nodes or not tets: |
| raise ValueError("Gmsh produced an empty mesh") |
| result["meshes"][str(size)] = {"nodes": nodes, "tets": tets} |
| finally: |
| gmsh.finalize() |
| return result |
|
|
|
|
| def dynamics(meshes: dict, setup: dict) -> dict: |
| import pychrono as ch |
| import pychrono.fea as fea |
| import numpy as np |
| from scipy.sparse import coo_matrix, diags |
| from scipy.sparse.linalg import eigsh |
|
|
| results = {} |
| for size, data in meshes.items(): |
| system = ch.ChSystemSMC() |
| system.SetGravitationalAcceleration(ch.ChVector3d(0, 0, 0)) |
| system.SetSolver(ch.ChSolverSparseLU()) |
| mesh = fea.ChMesh() |
| material = fea.ChContinuumElastic() |
| material.SetYoungModulus(setup["young_modulus_Pa"]) |
| material.SetPoissonRatio(setup["poisson_ratio"]) |
| material.SetDensity(setup["material_density_kg_m3"]) |
| keys = list(data["nodes"]) |
| node_index = {int(key): i for i, key in enumerate(keys)} |
| tip_ids = [key for key, point in data["nodes"].items() |
| if abs(point[0] - 0.1) < 1e-8] |
| fixed_ids = [key for key, point in data["nodes"].items() |
| if abs(point[0]) < 1e-8] |
| if len(tip_ids) < 4 or len(fixed_ids) < 4: |
| raise ValueError("Mesh is missing a clamp or load face") |
| nodes = {} |
| for key, point in data["nodes"].items(): |
| node = fea.ChNodeFEAxyz(ch.ChVector3d(*point)) |
| if key in fixed_ids: |
| node.SetFixed(True) |
| if key in tip_ids: |
| node.SetForce(ch.ChVector3d( |
| 0, 0, setup["tip_force_N"] / len(tip_ids))) |
| mesh.AddNode(node) |
| nodes[int(key)] = node |
| elements = [] |
| for a, b, c, d in data["tets"]: |
| element = fea.ChElementTetraCorot_4() |
| element.SetNodes(nodes[a], nodes[b], nodes[c], nodes[d]) |
| element.SetMaterial(material) |
| mesh.AddElement(element) |
| elements.append(((a, b, c, d), element)) |
| system.Add(mesh) |
| system.Setup() |
| rows, columns, values = [], [], [] |
| nodal_mass = np.zeros(len(keys)) |
| for tetrahedron, element in elements: |
| stiffness = element.GetStiffnessMatrix() |
| dofs = [3 * node_index[key] + axis |
| for key in tetrahedron for axis in range(3)] |
| for i in range(12): |
| for j in range(12): |
| value = stiffness.GetItem(i, j) |
| if value: |
| rows.append(dofs[i]) |
| columns.append(dofs[j]) |
| values.append(value) |
| points = np.array([data["nodes"][str(key)] |
| for key in tetrahedron]) |
| volume = abs(np.dot(points[1] - points[0], |
| np.cross(points[2] - points[0], |
| points[3] - points[0]))) / 6 |
| if volume <= 0: |
| raise ValueError("Invalid tetrahedron volume") |
| for key in tetrahedron: |
| nodal_mass[node_index[key]] += ( |
| setup["material_density_kg_m3"] * volume / 4) |
| matrix_size = 3 * len(keys) |
| full_stiffness = coo_matrix( |
| (values, (rows, columns)), |
| shape=(matrix_size, matrix_size)).tocsr() |
| active = [3 * i + axis for i, key in enumerate(keys) |
| if not nodes[int(key)].IsFixed() for axis in range(3)] |
| stiffness = full_stiffness[active, :][:, active] |
| mass = diags(np.repeat(nodal_mass, 3)[active]) |
| eigenvalues, _ = eigsh(stiffness, k=3, M=mass, |
| sigma=0, which="LM") |
| if min(eigenvalues) <= 0: |
| raise ValueError("Beam mode is not positive") |
| first_frequency = math.sqrt(min(eigenvalues)) / (2 * math.pi) |
| system.DoStaticLinear() |
| deflections = [data["nodes"][key][2] - nodes[int(key)].GetPos().z |
| for key in tip_ids] |
| mean_deflection = sum(deflections) / len(deflections) |
| if (not math.isfinite(mean_deflection) or mean_deflection <= 0 or |
| not math.isfinite(first_frequency)): |
| raise ValueError("Invalid beam mode or static deflection") |
| results[size] = { |
| "first_bending_frequency_hz": first_frequency, |
| "static_tip_deflection_m": mean_deflection, |
| "node_count": len(nodes), |
| "tetrahedron_count": len(data["tets"]), |
| "clamped_node_count": len(fixed_ids), |
| "loaded_node_count": len(tip_ids), |
| } |
| return results |
|
|
|
|
| def invoke(python: str, phase: str, payload: dict) -> dict: |
| run = subprocess.run([python, str(Path(__file__).resolve()), "--phase", phase], |
| input=json.dumps(payload), text=True, capture_output=True) |
| if run.returncode: |
| raise RuntimeError(f"{phase} failed:\n{run.stderr[-1600:]}") |
| return json.loads(run.stdout) |
|
|
|
|
| def main() -> None: |
| parser = argparse.ArgumentParser() |
| parser.add_argument("--cad-python", default=sys.executable) |
| parser.add_argument("--physics-python", default=sys.executable) |
| parser.add_argument("--phase", choices=("measure", "dynamics")) |
| args = parser.parse_args() |
| if args.phase: |
| payload = json.load(sys.stdin) |
| result = (measure(Path(payload["step"]), payload["setup"]) |
| if args.phase == "measure" |
| else dynamics(payload["meshes"], payload["setup"])) |
| print(json.dumps(result)) |
| return |
| setup = json.loads((ROOT / "setup.json").read_text()) |
| results = {} |
| for name in ("before", "after"): |
| properties = invoke(args.cad_python, "measure", { |
| "step": str(ROOT / f"{name}.step"), "setup": setup, |
| }) |
| meshes = properties.pop("meshes") |
| results[name] = { |
| "step_properties": properties, |
| "simulation_result": invoke(args.physics_python, "dynamics", { |
| "meshes": meshes, "setup": setup, |
| }), |
| } |
| before = results["before"] |
| after = results["after"] |
| bp, ap = before["step_properties"], after["step_properties"] |
| bs, gs = before["simulation_result"], after["simulation_result"] |
| sizes = [str(size) for size in setup["mesh_sizes_mm"]] |
| baseline = [bs[size]["first_bending_frequency_hz"] for size in sizes] |
| candidate = [gs[size]["first_bending_frequency_hz"] for size in sizes] |
| baseline_static = [bs[size]["static_tip_deflection_m"] for size in sizes] |
| candidate_static = [gs[size]["static_tip_deflection_m"] for size in sizes] |
| checks = { |
| "baseline_inside_forcing_band": all( |
| setup["forcing_band_hz"][0] <= value <= |
| setup["forcing_band_hz"][1] for value in baseline), |
| "first_mode_above_forcing_band": min(candidate) >= |
| setup["minimum_candidate_first_frequency_hz"], |
| "static_deflection_limited": max(candidate_static) <= |
| setup["maximum_candidate_static_tip_deflection_m"], |
| "mesh_response_stable": all( |
| abs(values[1] / values[0] - 1) <= limit |
| for values, limit in ( |
| (baseline, setup["maximum_relative_mesh_frequency_change"]), |
| (candidate, setup["maximum_relative_mesh_frequency_change"]), |
| (baseline_static, |
| setup["maximum_relative_mesh_deflection_change"]), |
| (candidate_static, |
| setup["maximum_relative_mesh_deflection_change"]))), |
| "mass_fixed": abs(ap["mass_kg"] / bp["mass_kg"] - 1) <= |
| setup["maximum_relative_mass_change"], |
| "end_pads_fixed": ap["end_pad_missing_mm3"] <= |
| setup["maximum_end_pad_missing_mm3"] and |
| ap["end_pad_excess_mm3"] <= setup["maximum_end_pad_excess_mm3"], |
| "envelope_fixed": ap["envelope_excess_mm3"] <= |
| setup["maximum_envelope_excess_mm3"], |
| } |
| after["comparison_to_before"] = { |
| "baseline_first_frequencies_hz": baseline, |
| "candidate_first_frequencies_hz": candidate, |
| "checks": checks, "passed": all(checks.values()), |
| } |
| for name, result in results.items(): |
| (ROOT / f"{name}.results.json").write_text(json.dumps(result, indent=2) + "\n") |
| print(f"First mode: {baseline} -> {candidate} Hz") |
| print(f"Static tip deflection: {baseline_static} -> {candidate_static} m") |
| print(f"Task passed: {all(checks.values())}") |
| if not all(checks.values()): |
| raise SystemExit(1) |
|
|
|
|
| if __name__ == "__main__": |
| main() |
|
|
