feat: adopt lumped mass and reduced-coordinate shell HHT

Integrate Hex8 mass verification and fixed-null-basis shell dynamics with numerical and physics handoff evidence. Preserve interrupted reference and full-validation status; full integration validation is deferred until after performance optimization.

include/fesa/elements/nonlinear_mitc4_shell.h

@@ -2,6 +2,7 @@
 #define FESA_ELEMENTS_NONLINEAR_MITC4_SHELL_H_
 
 #include <array>
+#include <cstddef>
 #include <string>
 
 #include "fesa/core/status.h"
@@ -53,6 +54,22 @@ struct NonlinearMitc4InternalEquilibrium {
   Matrix drilling_constraint_gradient{0U, 0U};
   std::array<Matrix, 4> drilling_constraint_hessian{
       Matrix{0U, 0U}, Matrix{0U, 0U}, Matrix{0U, 0U}, Matrix{0U, 0U}};
+  std::array<Vector, 4> drilling_constraint_third_directional_gradient{
+      Vector{0U}, Vector{0U}, Vector{0U}, Vector{0U}};
+};
+
+/// @brief Stores one nodal external drilling-null scalar and its variations.
+/// @note The scalar is `-n(phi)^T F`, where `n` is the normalized physical
+/// drill-null direction. Directional fields use `W=(phi_dot, 1)` and include
+/// the supplied force time derivatives.
+struct NonlinearMitc4ExternalDrillingConstraint {
+  double value = 0.0;
+  Vector gradient{0U};
+  Matrix hessian{0U, 0U};
+  double directional_first = 0.0;
+  double directional_second = 0.0;
+  Vector gradient_directional_first{0U};
+  Vector gradient_directional_second{0U};
 };
 
 class NonlinearMitc4Shell;
@@ -95,6 +112,22 @@ class NonlinearMitc4Shell {
   [[nodiscard]] Result<NonlinearMitc4Recovery> RecoverState(
       const NonlinearMitc4TrialDofs& trial) const;
 
+  /// @brief Evaluates the external nodal drill-null scalar through W.
+  /// @param node Source-local node index in `[0, 4)`.
+  /// @param phi Fixed-global principal-chart rotation in radians.
+  /// @param phi_dot Fixed-global chart rate in radians per time.
+  /// @param force Nodal external generalized moment.
+  /// @param force_rate First time derivative of force.
+  /// @param force_acceleration Second time derivative of force.
+  /// @return The scalar `-n(phi)^T force` and exact coordinate/time
+  /// derivatives, or a fail-closed diagnostic.
+  [[nodiscard]] Result<NonlinearMitc4ExternalDrillingConstraint>
+  EvaluateExternalDrillingConstraint(std::size_t node, const Vector3& phi,
+                                     const Vector3& phi_dot,
+                                     const Vector3& force,
+                                     const Vector3& force_rate,
+                                     const Vector3& force_acceleration) const;
+
  private:
   /// @brief Retains validated fixed-reference data without analysis ownership.
   NonlinearMitc4Shell(std::array<Vector3, 4> coordinates,