feat(analysis): implement Hex8 solid static procedures

include/fesa/analysis/solid_static_procedure.h

@@ -0,0 +1,39 @@
+#ifndef FESA_ANALYSIS_SOLID_STATIC_PROCEDURE_H_
+#define FESA_ANALYSIS_SOLID_STATIC_PROCEDURE_H_
+
+#include "fesa/analysis/solid_static_state.h"
+
+namespace fesa {
+class LinearSolver;
+class ParallelFor;
+class TangentSolver;
+
+/// @brief Owns successful static frames and sorted model diagnostics.
+struct SolidStaticExecutionResult {
+  SolidStaticState state;
+  std::vector<Diagnostic> diagnostics;
+};
+
+/// @brief Executes linear K0 or fixed-factor TL StVK static analysis.
+class SolidStaticProcedureExecutor {
+ public:
+  /// @brief Uses non-owned adapters, which must outlive this executor.
+  /// @param tangent_solver Must support indefinite stressed tangents.
+  SolidStaticProcedureExecutor(const ParallelFor& parallel_for,
+                               LinearSolver& linear_solver,
+                               TangentSolver& tangent_solver);
+  /// @brief Returns validated results; no I/O or final-file replacement.
+  Result<SolidStaticExecutionResult> Execute(const Domain& domain) const;
+  /// @brief Executes into a fresh observer retaining accepted history on
+  /// failure.
+  /// @note A previously initialized observer is rejected without mutation.
+  Status ExecuteInto(const Domain& domain, SolidStaticState& state) const;
+
+ private:
+  const ParallelFor& parallel_for_;
+  LinearSolver& linear_solver_;
+  TangentSolver& tangent_solver_;
+};
+}  // namespace fesa
+
+#endif  // FESA_ANALYSIS_SOLID_STATIC_PROCEDURE_H_