solver: nonlinear static analysis by Newton–Raphson with automatic increments

solve.nonlinear follows a nonlinear static step in load increments: dead
loads and prescribed displacements ramp with the load factor, a pressure
follows the deformed faces (its load stiffness symmetrised so the
supernodal Cholesky stays), the consistent tangent is refactored every
iteration with an optional line search, and an increment converges on
force, displacement and energy together. Increments start from the
extrapolated last one, grow after fast convergence and are cut back on
inversion, a non-finite or growing residual, an indefinite tangent or too
many iterations; the step stops cleanly at the minimum increment, the
increment cap or the Newton iteration limit. Elements are assembled in
parallel in label order (same bits on any thread count). Results carry
Cauchy stress, logarithmic strain, the increment history and a displacement
frame per increment, which results.frame and the results panel show.
Trusses, shells, beams, plane stress, incompatible modes, temperature and
centrifugal loads are refused by name; couplings warn that they stay
linear.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

crates/solver/src/lib.rs

@@ -31,6 +31,7 @@ pub mod constraints;
 pub mod discrete;
 pub mod eigen;
 pub mod heat;
+pub mod nonlinear;
 pub mod ordering;
 pub mod sparse;
 pub mod system;
@@ -40,6 +41,7 @@ pub use analysis::{
     solve_static,
 };
 pub use heat::{HeatResult, solve_heat};
+pub use nonlinear::solve_nonlinear;
 
 #[derive(Debug, Clone, PartialEq, thiserror::Error)]
 pub enum Error {
@@ -82,16 +84,24 @@ pub struct Limits {
     pub max_factor_entries: usize,
     /// Lanczos vectors (iterations × block size).
     pub max_lanczos_vectors: usize,
+    /// Newton iterations of a nonlinear step, over all its increments.
+    pub max_newton_iterations: usize,
 }
 
 impl Limits {
     pub const MAX_DOFS: usize = 6_000_000;
     pub const MAX_FACTOR_ENTRIES: usize = 400_000_000;
     pub const MAX_LANCZOS_VECTORS: usize = 3_000;
+    pub const MAX_NEWTON_ITERATIONS: usize = 100_000;
 }
 
 impl Default for Limits {
     fn default() -> Limits {
-        Limits { max_dofs: Limits::MAX_DOFS, max_factor_entries: Limits::MAX_FACTOR_ENTRIES, max_lanczos_vectors: Limits::MAX_LANCZOS_VECTORS }
+        Limits {
+            max_dofs: Limits::MAX_DOFS,
+            max_factor_entries: Limits::MAX_FACTOR_ENTRIES,
+            max_lanczos_vectors: Limits::MAX_LANCZOS_VECTORS,
+            max_newton_iterations: Limits::MAX_NEWTON_ITERATIONS,
+        }
     }
 }