Update test_cantilever_regression.jl to use new DOF system, DOFManager,
and proper constraint elimination instead of old Physics struct API.
- Create elements using new @DOFSet and Element{K,P,S} API
- Use DOFManager for DOF allocation and management
- Apply forces using get_node_dofs API instead of NeumannBC
- Apply boundary conditions using constraint elimination (proper method)
- Solve reduced system (K_ff * u_f = f_f) instead of manipulating full matrix
- Reconstruct full solution from reduced solution
- Remove old Physics struct, DirichletBC, NeumannBC usage
- Update step numbering and comments for clarity
- Implement full 3D cantilever beam FEM validation
- Test LinearElastic material with known analytical solution
- Verify tip displacement against reference value
- Test assembly pipeline from mesh to solution
- Include boundary conditions (fixed end, tip load)
- Validate solver convergence and accuracy
- Document expected displacement and tolerance
- Serve as integration test for complete FEM workflow
- 359 lines of end-to-end validation test
Jukka Aho