initial commit FESurrogateModelTutorial

FESurrogateModelTutorial/src/femsurrogate/fea/solver.py

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+import numpy as np
+from scipy.sparse.linalg import spsolve
+
+from femsurrogate.fea.assembly import (
+    assemble_global_stiffness,
+    assemble_load_vector,
+    constrained_dofs,
+    node_ids,
+)
+from femsurrogate.fea.model import BeamModel, Displacement
+
+
+def solve_linear_static(model: BeamModel) -> dict[int, Displacement]:
+    stiffness = assemble_global_stiffness(model)
+    loads = assemble_load_vector(model)
+    fixed = np.array(constrained_dofs(model), dtype=int)
+    all_dofs = np.arange(loads.size)
+    free = np.setdiff1d(all_dofs, fixed, assume_unique=True)
+
+    displacements = np.zeros_like(loads)
+    displacements[free] = spsolve(stiffness[free][:, free], loads[free])
+
+    result: dict[int, Displacement] = {}
+    for position, node_id in enumerate(node_ids(model)):
+        base = position * 3
+        result[node_id] = Displacement(
+            node_id=node_id,
+            ux=float(displacements[base]),
+            uy=float(displacements[base + 1]),
+            rz=float(displacements[base + 2]),
+        )
+
+    return result