UW Composites Analysis · Laminate Builder
Classical Laminate Theory and ABD Matrix Calculator
Build a composite laminate ply by ply, or type a stacking sequence such as [0/45/−45/90]s, and see how it responds. The Laminate Builder computes the A, B and D matrices from classical laminate theory, the equivalent laminate moduli, and the stiffness in every direction, live as you change the layup.
Open the Laminate Builder →Free, runs in your browser, no installation or login.
What you can do
- Arrange plies and angles, or enter a stacking sequence in standard notation.
- Read the extensional (A), coupling (B) and bending (D) stiffness matrices, and see whether a layup has bending–extension coupling.
- Get the equivalent moduli Ex, Ey, Gxy and νxy, plus thickness, areal mass and raw material cost.
- Inspect a polar plot of laminate stiffness by direction, and pick any ply to see its orientation.
How it works
A = Σ Q̄k (zk − zk−1), B = ½ Σ Q̄k (zk² − zk−1²), D = ⅓ Σ Q̄k (zk³ − zk−1³)
Laminate stiffness from the transformed ply stiffness Q̄ of each ply k between its interfaces z.
{N ; M} = [A B ; B D] {ε⁰ ; κ}
Forces and moments per unit width from midplane strains and curvatures.
Ex = 1/(h a11), Ey = 1/(h a22), Gxy = 1/(h a66), νxy = −a12/a11
Equivalent in-plane laminate moduli, with a = A⁻¹ and laminate thickness h.
Ply properties come from the Material Builder (micromechanics of the chosen fiber, resin and fiber volume fraction). The laminate equations are standard classical laminate theory. Every page of the app lists its full equations and sources under Equations.
Questions to explore
- Why does a quasi-isotropic laminate have the same in-plane stiffness in every direction?
- What happens to the B matrix when a layup is no longer symmetric, and why does that make a flat panel warp?
- How much do ±45° plies add to the shear modulus, and what do they cost in axial stiffness?