feat(solid): add Hex8 input and three-DOF semantics

include/fesa/fem/dof_manager.h

@@ -16,8 +16,8 @@ namespace fesa {
 
 class DofManagerTestAccess;
 
-/// @brief Distinguishes structural six-component and thermal five-station maps.
-enum class DofProfile { kStructural, kThermal };
+/// @brief Distinguishes six-component, Solid translation, and thermal maps.
+enum class DofProfile { kStructural, kThermal, kSolidStructural };
 
 /// @brief Stores the stable full-space CSR pattern.
 struct SparsePattern {
@@ -59,6 +59,8 @@ class DofManager {
 
   /// @brief Reports which physical component profile owns this mapping.
   DofProfile Profile() const noexcept;
+  /// @brief Returns the physical component count for the active profile.
+  std::size_t ComponentsPerNode() const noexcept;
 
   /// @brief Returns the full node-by-component DOF count.
   std::size_t FullDofCount() const noexcept;