feat(geometry): Add strain computation function

- Implement compute_strain() for small strain tensor calculation
- Zero allocation with NTuple inputs and Tensors.jl
- Type stable (@inferred passes)
- Complete test suite with 4 test cases (uniaxial, shear, rigid body, performance)
- Performance validated: 0 allocations, ~110ns median
- Add to test suite in runtests.jl
- Export from JuliaFEM module

Resolves user story #0001
This commit is contained in:
Jukka Aho
2025-11-12 02:19:45 +02:00
parent f350b707cf
commit c40fcdbb91
4 changed files with 154 additions and 0 deletions
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# This file is part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE
"""
Strain computation utilities for finite element analysis.
This module provides functions for computing strain tensors from nodal
displacements and basis function derivatives.
"""
using Tensors
"""
compute_strain(u_elem, dN_dx) -> SymmetricTensor{2,3}
Compute small strain tensor from nodal displacements.
Small strain: ε = ½(∇u + ∇u^T) where ∇u = ∑ᵢ uᵢ ⊗ (dNᵢ/dx)
# Arguments
- `u_elem::NTuple{N, Vec{3}}`: Nodal displacement vectors
- `dN_dx::NTuple{N, Vec{3}}`: Basis derivatives in physical coordinates
# Returns
- `ε::SymmetricTensor{2,3}`: Small strain tensor
# Example
```julia
u = (Vec{3}((0.1, 0.0, 0.0)), Vec{3}((0.15, 0.02, 0.0)))
dN_dx = (Vec{3}((-1.0, -1.0, -1.0)), Vec{3}((1.0, 0.0, 0.0)))
ε = compute_strain(u, dN_dx)
```
"""
function compute_strain(
u_elem::NTuple{N,Vec{3}},
dN_dx::NTuple{N,Vec{3}}
) where N
# Displacement gradient: ∇u = ∑ᵢ uᵢ ⊗ (dNᵢ/dx)
∇u = sum(u_i ⊗ dN_i for (u_i, dN_i) in zip(u_elem, dN_dx))
# Small strain (symmetric part): ε = ½(∇u + ∇u^T)
ε = symmetric(∇u)
return ε
end