feat: implement consistent-mass HHT shell dynamics

include/fesa/analysis/hht_time_integration.h

@@ -0,0 +1,50 @@
+#ifndef FESA_ANALYSIS_HHT_TIME_INTEGRATION_H_
+#define FESA_ANALYSIS_HHT_TIME_INTEGRATION_H_
+
+#include "fesa/core/status.h"
+#include "fesa/math/vector.h"
+
+namespace fesa {
+
+/// @brief Stores the coupled original negative-alpha HHT coefficients.
+struct HhtParameters {
+  double alpha;
+  double beta;
+  double gamma;
+};
+
+/// @brief Stores the displacement and velocity Newmark predictors.
+struct HhtPredictor {
+  Vector coordinates;
+  Vector velocity;
+};
+
+/// @brief Separates physical chart rates from the auxiliary acceleration.
+struct HhtRates {
+  Vector velocity;
+  Vector acceleration;
+  Vector algorithmic_acceleration;
+};
+
+/// @brief Builds coupled coefficients for alpha in [-1/3, 0].
+/// @note The public INP subset uses only alpha=-0.05.
+Result<HhtParameters> MakeHhtParameters(double alpha);
+
+/// @brief Predicts q and v using the old auxiliary acceleration.
+/// @param time_increment Finite positive duration in input time units.
+Result<HhtPredictor> PredictHht(const Vector& coordinates,
+                              const Vector& velocity,
+                              const Vector& algorithmic_acceleration,
+                              double time_increment,
+                              const HhtParameters& parameters);
+
+/// @brief Recovers physical and auxiliary rates from one trial coordinate.
+/// @param old_acceleration Physical endpoint acceleration at the old time.
+Result<HhtRates> EvaluateHhtRates(const Vector& coordinates,
+                                const HhtPredictor& predictor,
+                                const Vector& old_acceleration,
+                                double time_increment,
+                                const HhtParameters& parameters);
+
+}  // namespace fesa
+#endif  // FESA_ANALYSIS_HHT_TIME_INTEGRATION_H_