FEM foundation B: heat transfer and thermal stress (solids, 2D, explicit), coupled temperature–displacement, solve.heat (#45)

* Heat transfer and thermal stress: thermal materials, temperature BCs, heat loads, heat transfer and coupled temperature–displacement steps, solve.heat

Model: Material.thermal (conductivity, specific heat, expansion, isotropic or
per axis; reference temperature), BoundaryCondition::Temperature (dof 11),
loads SurfaceFlux, Convection, HeatSource and Temperature (a field in static
steps), procedures HeatTransfer { transient (θ-method) } and
CoupledTemperatureDisplacement; checks for missing conductivity/specific
heat/expansion. fem: heat conduction kernels (conductivity, capacity,
source, face flux/film, heat flux) on the DofLayout (one T per node), thermal
strain load and stress D(ε − ε_th) for every solid formulation incl.
incompatible modes. Solver: steady and transient heat transfer, thermal loads
in static steps, coupled steps (exact one-way coupling). Engine: solve.heat,
temperature/heat-flux result fields, probes. Decks refuse heat transfer by
name. Analytic verification: slab, source+convection/flux, thick cylinder,
erfc semi-infinite solid, free/constrained expansion, bimetal strip, coupled
step.

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

* thermal: strains in 2D elements and explicit dynamics

Plane::thermal_load and stresses_with for plane stress (εzz free), plane
strain (σzz = −D₃·ε_th) and axisymmetric elements, incompatible modes
included; the solver's 2D kernels take them. Explicit dynamics turns a
step's temperature loads into a per-element thermal strain rate (reached
linearly over the step) subtracted from each strain increment, so it feeds
J2 and Johnson–Cook updates. Verified: free expansion in every 2D theory
and element, a biaxially held plate, an explicit free bar (ΔL = αΔT L,
stress-free) and a clamped bar at −EαΔT, capped at the yield stress with
perfect plasticity.

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

* clippy

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

* thermal: trusses take the axial thermal strain; keep the roadmap's M7 line

Truss::thermal_load and stresses_with project the thermal strain on the
member's tangent (Σ αₖ tₖ² ΔT); the static solver applies them to rod2/rod3
(#38). Explicit trusses take none yet and a warning says so.

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

---------

Co-authored-by: jyviko <2501648+jyviko@users.noreply.github.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

crates/ui-egui/src/results.rs

@@ -69,16 +69,19 @@ impl Plot {
     pub fn mode(&self) -> Option<(usize, f64)> {
         match self.result.kind() {
             Kind::Frequency(f) => f.modes.get(self.pick.mode.checked_sub(1)?).map(|m| (self.pick.mode, m.frequency)),
-            Kind::Static(_) | Kind::Explicit(_) | Kind::Fluid(_) => None,
+            Kind::Static(_) | Kind::Explicit(_) | Kind::Fluid(_) | Kind::Heat(_) => None,
         }
     }
 
-    /// An explicit step's field frame shown, its time and the number of frames.
+    /// An explicit or transient heat step's frame shown, its time and the number of frames.
     pub fn frame(&self) -> Option<(usize, f64, usize)> {
-        let Kind::Explicit(e) = self.result.kind() else { return None };
-        let n = e.frames.len();
+        let (n, time): (usize, &dyn Fn(usize) -> Option<f64>) = match self.result.kind() {
+            Kind::Explicit(e) => (e.frames.len(), &|k| e.frames.get(k).map(|f| f.time)),
+            Kind::Heat(h) if h.times.len() > 1 => (h.times.len(), &|k| h.times.get(k).copied()),
+            _ => return None,
+        };
         let k = self.pick.frame.unwrap_or(n.checked_sub(1)?);
-        Some((k, e.frames.get(k)?.time, n))
+        Some((k, time(k)?, n))
     }
 
     /// The node's position in the plot, if it is drawn.
@@ -107,7 +110,7 @@ pub fn swing(result: &StepResult, frame: Option<u64>) -> f64 {
     match result.kind() {
         Kind::Frequency(_) => a.sin(),
         Kind::Static(_) => 0.5 * (1.0 - a.cos()),
-        Kind::Explicit(_) | Kind::Fluid(_) => 1.0,
+        Kind::Explicit(_) | Kind::Fluid(_) | Kind::Heat(_) => 1.0,
     }
 }