"""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()