Add caching for flex stiffness computation.

This change introduces methods to cache and load the computed stiffness matrix and nodal masses for flex elements. The cache key is generated based on material properties (Young's modulus, Poisson's ratio), interpolation order, and the bounding box of the flex. This avoids redundant expensive computations when compiling models with identical flex definitions.

PiperOrigin-RevId: 874689771
Change-Id: I6d1e299baf294a984b507e2a2602b2c068610536

src/user/user_objects.h

@@ -992,6 +992,9 @@ class mjCFlex_ : public mjCBase {
   std::vector<int> spec_elem_;
   std::vector<float> spec_texcoord_;
   std::vector<int> spec_elemtexcoord_;
+
+  // caching
+  std::vector<double> cached_stiffness_;   // cached stiffness matrix
 };
 
 class mjCFlex: public mjCFlex_, private mjsFlex {
@@ -1040,6 +1043,11 @@ class mjCFlex: public mjCFlex_, private mjsFlex {
   std::vector<double> node0_;             // node Cartesian positions
 
   int order_ = 0;                         // interpolation order
+
+  // stiffness caching
+  std::string ComputeStiffnessCacheKey() const;
+  bool LoadCachedStiffness();
+  void CacheStiffness();
 };