Inputs
Example Data Table
| Layup | Ply t (mm) | E1 (GPa) | E2 (GPa) | G12 (GPa) | ν12 | Approx outputs |
|---|---|---|---|---|---|---|
| [0/90]s | 0.125 | 135 | 10 | 5 | 0.30 | h≈0.5 mm, Ex≈52.4 GPa, Gxy≈20.0 GPa |
| [0]8 | 0.125 | 135 | 10 | 5 | 0.30 | High Ex, low Ey; strong directional behavior |
| [+45/-45]s | 0.125 | 135 | 10 | 5 | 0.30 | Higher shear stiffness; balanced in-plane coupling |
Formula Used
This calculator uses Classical Lamination Theory (CLT). Each ply has a reduced stiffness matrix Q in its material axes, transformed to the laminate axes as Q̄ using the ply angle.
Q22 = E2 / (1 − ν12·ν21)
Q12 = ν12·E2 / (1 − ν12·ν21)
Q66 = G12 , ν21 = ν12·E2/E1
Through-thickness integration forms the laminate stiffness matrices:
B = 1/2 · Σ(Q̄k · (zk² − zk−1²))
D = 1/3 · Σ(Q̄k · (zk³ − zk−1³))
Effective in-plane properties use the compliance matrix a = A⁻¹: Ex = 1/(a11·h), Ey = 1/(a22·h), Gxy = 1/(a66·h), and νxy = −a12/a11.
How to Use This Calculator
- Enter the number of plies you want to define.
- Fill each ply row with thickness, elastic constants, and angle.
- Enable “symmetric” if you entered only half the stack.
- Optional: enter width and length for beam/strip stiffness.
- Click Calculate to see A/B/D matrices and effective moduli.
- Use CSV or PDF buttons to export the computed report.
Composite Stiffness Guide
1) Why Composite Stiffness Matters
Composite laminates let you “place” stiffness where a structure needs it. A 1.0 mm laminate with a mostly 0° layup can behave like a very stiff strip along its length, while the same thickness with more 90° plies can prioritize transverse rigidity. Small layup changes can shift deflection, buckling margin, and vibration response.
2) CLT Inputs and Units
Each ply is defined by orthotropic properties: E1, E2, G12, and ν12, plus thickness and angle. Typical carbon/epoxy data used in quick checks are E1≈135 GPa, E2≈10 GPa, G12≈5 GPa, ν12≈0.30, with t≈0.125 mm per ply. Keep moduli in GPa and thickness in mm.
3) Ply Orientation Effects
The angle rotates stiffness into the global laminate axes. 0° plies dominate Ex, 90° plies dominate Ey, and ±45° plies strongly influence Gxy and shear-driven deformations. A balanced layup like [0/±45/90]s often yields stable in-plane behavior for plates and shells.
4) Thickness and Laminate Symmetry
Bending stiffness scales rapidly with thickness: for many cases, doubling total thickness increases bending terms roughly by a factor of eight because D depends on z³. Symmetric laminates (for example, [0/90]s) tend to have B≈0, meaning less bending–extension coupling and more predictable deflection.
5) Understanding A, B, D Matrices
The in-plane matrix A (units N/m) controls membrane forces, D (N·m) controls bending moments, and B represents coupling. If your laminate is not symmetric, a pure in-plane load can induce bending and twist, which is visible as non-zero B terms.
6) Effective Engineering Constants
The calculator reports effective Ex, Ey, Gxy, and νxy derived from the in-plane compliance A⁻¹. As a quick sanity check, Ex should be between E2 and E1 for most layups, and balanced laminates typically produce modest νxy values.
7) Beam/Strip Stiffness Outputs
When width and length are provided, the tool converts laminate stiffness to strip-style measures such as axial rigidity EA and bending rigidity EI. For a simply supported case, the midspan deflection under a point load roughly follows δ ∝ PL³/(EI), so accurate geometry inputs matter.
8) Practical Data Checks and Validation
Use the example table as a baseline and compare results across layups. If you swap 0° and 90° plies, expect Ex and Ey to trade roles. If you mirror the stack, B should trend toward zero. For critical work, validate against a laminate handbook or FEA.
FAQs
1) What does “composite stiffness” mean here?
It refers to laminate resistance to in-plane stretching, shear, bending, and coupling, summarized by the CLT A, B, and D matrices and reported as effective engineering constants.
2) What if I don’t know the shear modulus G12?
Use a datasheet value if possible. For rough estimates, G12 is often 3–6 GPa for common carbon/epoxy systems, but uncertainty can noticeably affect Gxy and shear-dominated deflections.
3) Why is the symmetric option useful?
Symmetry makes the coupling matrix B approach zero, reducing bending–extension coupling. It also lets you enter half the stack and mirror it, saving time and reducing input errors.
4) What does a nonzero B matrix indicate?
It indicates coupling between membrane loads and bending/twisting. Non-symmetric stacking sequences can bend under in-plane tension or develop in-plane strains under bending moments.
5) How many plies can I model?
The calculator supports up to 20 plies. If you need more, combine identical adjacent plies by summing thickness, or model a repeating block to approximate the full stack.
6) How are Ex and Ey computed from the laminate?
They are derived from the inverse of the in-plane stiffness matrix, a = A⁻¹, using Ex = 1/(a11·h) and Ey = 1/(a22·h), where h is total laminate thickness.
7) Can I use this for sandwich panels?
Partially. You can approximate facesheets by entering their plies, but true sandwich behavior depends on core shear stiffness and face–core spacing. For accurate results, use a dedicated sandwich model.