Results & Outputs
After defining the laminate and loads, all results are computed in real time. The results display shows ply-level detail at three through-thickness locations per ply.
Mid-Plane Strains & Curvatures
The mid-plane strains (ε⁰x, ε⁰y, γ⁰xy) and curvatures (κx, κy, κxy) are the primary unknowns in CLT. They are obtained by inverting the ABD system.
Note: For symmetric laminates ([B] = 0), in-plane loads produce only mid-plane strains and bending moments produce only curvatures. For non-symmetric laminates, the coupling matrix [B] produces coupled behavior.
Ply-Level Strains & Stresses
For each ply, strains and stresses are reported at three through-thickness locations:
- Top (Outer) — Upper/outer surface of the ply (z = zk-1)
- Mid — Center of the ply (z = (zk-1 + zk)/2)
- Bot (Inner) — Lower/inner surface of the ply (z = zk)
Results are presented in two coordinate systems:
- Laminate (x-y) — Global coordinate strains (εx, εy, γxy) and stresses (σx, σy, τxy)
- Material (1-2) — Fiber-aligned strains (ε₁, ε₂, γ₁₂) and stresses (σ₁, σ₂, τ₁₂), obtained by rotating through the ply angle θ
Laminate Strain at Depth z
εx(z)εy(z)γxy(z) | = | ε⁰xε⁰yγ⁰xy | + z · | κxκyκxy |
Laminate Stress (x-y)
σxσyτxy | = | Q̄₁₁Q̄₁₂Q̄₁₆Q̄₁₂Q̄₂₂Q̄₂₆Q̄₁₆Q̄₂₆Q̄₆₆ | · | εx(z)εy(z)γxy(z) |
Material Stress (1-2)
σ₁σ₂τ₁₂ | = | Q₁₁Q₁₂0Q₁₂Q₂₂000Q₆₆ | · | ε₁ε₂γ₁₂ |
Stress Transformation (x-y → 1-2)
σ₁σ₂τ₁₂ | = | m²n²2mnn²m²−2mn−mnmnm²−n² | · | σxσyτxy |
Strain Transformation (x-y → 1-2)
ε₁ε₂γ₁₂ | = | m²n²mnn²m²−mn−2mn2mnm²−n² | · | εxεyγxy |
where m = cos(θ), n = sin(θ), and θ is the ply angle
Material coordinate values are used for failure evaluation, since composite failure is governed by fiber-direction and transverse-direction mechanisms.
Workbook Export & CSV
The results can be exported in two formats:
- Workbook View — An interactive tabular display that mirrors the layout of the Composite_Laminates.xlsm spreadsheet for direct comparison.
- CSV Export — Downloads the full ply-by-ply results as a CSV file for use in external tools or reports.