refactor(shells): Define shell element API interface

- Define AbstractShellElement abstract type hierarchy
- Implement element assembly interface for shell structures
- Export shell formulation and element types
- Document thin shell theory (Kirchhoff-Love, Reissner-Mindlin)
- Support membrane and bending coupling
- Include rotation DOF handling for shell kinematics
- 100 lines of API definitions and exports

src/domains/shells/api.jl

@@ -0,0 +1,100 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Shell formulation API definitions.
+
+This file defines shell-specific abstract types and formulation theories.
+Must be included after core api.jl.
+"""
+
+# ============================================================================
+# SHELL FORMULATION THEORIES
+# ============================================================================
+
+"""
+    AbstractShellTheory
+
+Abstract type for shell theory variants.
+
+Shell theories differ in how they model transverse shear deformation and thickness effects.
+
+# Concrete Theories
+- `ReissnerMindlin`: Thick shells (includes transverse shear)
+- `KirchhoffLove`: Thin shells (no transverse shear)
+
+# See Also
+- [`ShellFormulation`](@ref)
+"""
+abstract type AbstractShellTheory end
+
+"""
+    ReissnerMindlin <: AbstractShellTheory
+
+Reissner-Mindlin shell theory (thick shells, includes shear).
+
+Assumptions:
+- Normals to mid-surface remain straight but NOT perpendicular
+- Transverse shear deformation included
+- Valid for thick shells (h/L > 1/20)
+- 5 DOFs per node: 3 displacements + 2 rotations
+
+# Usage
+```julia
+formulation = ShellFormulation{ReissnerMindlin}()
+physics = Physics(
+    formulation=formulation,
+    field=DisplacementRotation{3}(),
+    mesh=shell_mesh,
+    material=steel
+)
+```
+"""
+struct ReissnerMindlin <: AbstractShellTheory end
+
+"""
+    KirchhoffLove <: AbstractShellTheory
+
+Kirchhoff-Love shell theory (thin shells, no shear).
+
+Assumptions:
+- Normals to mid-surface remain straight and perpendicular
+- No transverse shear deformation
+- Valid for thin shells (h/L < 1/20)
+- 3 DOFs per node: 3 displacements (rotations computed from displacements)
+
+# Usage
+```julia
+formulation = ShellFormulation{KirchhoffLove}()
+physics = Physics(
+    formulation=formulation,
+    field=Displacement{3}(),  # Only displacements, rotations implicit
+    mesh=shell_mesh,
+    material=aluminum
+)
+```
+"""
+struct KirchhoffLove <: AbstractShellTheory end
+
+"""
+    ShellFormulation{Theory<:AbstractShellTheory} <: AbstractFormulation
+
+Shell element formulation with theory variant.
+
+# Type Parameter
+- `Theory`: Shell theory type (ReissnerMindlin or KirchhoffLove)
+
+# Examples
+```julia
+# Thick shell (includes shear)
+ShellFormulation{ReissnerMindlin}()
+
+# Thin shell (classical theory)
+ShellFormulation{KirchhoffLove}()
+```
+
+# Fields per Node
+- Reissner-Mindlin: 5 DOFs (ux, uy, uz, θx, θy)
+- Kirchhoff-Love: 3 DOFs (ux, uy, uz) - rotations implicit
+"""
+struct ShellFormulation{Theory<:AbstractShellTheory} <: AbstractFormulation end