LamIO
Classical Laminate TheoryFree CLT laminate calculator for composite layups and sandwich panels. ABD matrices, ply strains, effective moduli, and polar plots.
Laminate Type
Materials
Composite ply presets below; metallic face sheets often use MMPDS 2024-T3 (E ≈ 10,600 ksi) in sandwich designs.
Ply Stack
Bottom → top. Symmetric layups give B ≈ 0.
| # | t (in) | θ (°) |
|---|
Top Face Plies
| # | t (in) | θ (°) |
|---|
Bottom Face Plies
Bottom → top (stacked upward toward the core).
| # | t (in) | θ (°) |
|---|
Core (isotropic)
Loads (per unit width)
Qx, Qy (transverse shear, lb/in) are omitted — standard CLT assumes normals stay straight and neglects through-thickness shear. They matter for thick laminates, sandwich core shear, or FSDT; LamIO uses the {N, M} ↔ {ε⁰, κ} system only.
Failure Check
Layup Preview
Laminate Summary
Laminate Polar Plot
Effective extensional moduli vs laminate orientation (0–360°). A circle indicates quasi-isotropy.
[A] (lb/in)
[B] (lb)
[D] (lb-in)
Midplane Response
Ply Strains & Stresses
| Ply | θ | z (in) | εₓ (με) | εᵧ (με) | γₓᵧ (με) | ε₁ (με) | ε₂ (με) | γ₁₂ (με) | σ₁ | σ₂ | τ₁₂ | FI |
|---|
Define your layup and click SOLVE to run CLT analysis.
Technical Reference
LamIO — Classical Laminate Theory
Jones / Kaw — plane stress • Moduli/stresses in ksi; loads in lb/in & lb-in/in; [A] in lb/in, [B] in lb, [D] in lb-in. Strains reported as με.
LamIO assembles the laminate stiffness matrices [A], [B], and [D] from ply reduced stiffness [Q] transformed to [Q̄] at each orientation. Resultant loads {N, M} are related to midplane strains {ε⁰} and curvatures {κ} through the coupled system. Use this to evaluate extension, bending, coupling, and per-ply material strains under applied loads.
Governing Equations
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Constitutive relation
{N} = [A]{ε⁰} + [B]{κ}, {M} = [B]{ε⁰} + [D]{κ}
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Ply integration
Aᵢⱼ = Σ Q̄ᵢⱼ⁽ᵏ⁾(zₖ − zₖ₋₁), Bᵢⱼ = ½Σ Q̄ᵢⱼ⁽ᵏ⁾(zₖ² − zₖ₋₁²), Dᵢⱼ = ⅓Σ Q̄ᵢⱼ⁽ᵏ⁾(zₖ³ − zₖ₋₁³). z measured from laminate midplane.
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Ply strains
{ε}ₓᵧ(z) = {ε⁰} + z{κ}. Material strains {ε}₁₂ obtained via strain transformation at ply angle θ.
Features
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Solid laminate
Arbitrary ply stack bottom-to-top. Symmetric layups (mirror about midplane) produce B ≈ 0 and decouple extension from bending.
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Sandwich panel
Bottom face + isotropic core + top face. Core modeled as a 0° isotropic ply (E₁ = E₂ = E). Mirror duplicates top plies for the bottom skin; uncheck to define a separate bottom stack.
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Effective moduli
Ēₓ = 1/(h·a₁₁), Ēᵧ = 1/(h·a₂₂), Ḡₓᵧ = 1/(h·a₆₆) from [A]⁻¹. Quasi-isotropic flag when Ēₓ/Ēᵧ ≈ 1 (±8%).
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Polar plot
Laminate Ēx, Ēy, Ḡxy vs orientation (0–360°). A near-circular trace indicates quasi-isotropic extensional response.
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Failure criteria
Max fiber strain, max stress, Tsai-Hill, or Tsai-Wu. When enabled, the ply table shows the outer two plies only (one row per ply; FI uses the governing surface). FI ≤ 1 is PASS.
Linear elastic CLT only. No progressive failure, no interlaminar shear, no transverse shear in sandwich (thin-face assumption). Verify critical plies with test data or more advanced failure theories (Tsai-Wu, Hashin).