Free Composite Laminate Calculator

It turns plies into a plate

Classical Lamination Theory takes what you know about a single ply - E₁, E₂, G₁₂, v₁₂, its thickness and its angle - and predicts how the whole stack behaves. It has been the workhorse of composite design since the 1960s, and it rests on three assumptions: the laminate is thin compared to its width, out-of-plane stresses are negligible (plane stress), and the plies are perfectly bonded so strain runs continuously through the thickness.

Every ply gets rotated into a shared frame

A ply is stiff along its fibers (the 1 direction) and soft across them (the 2 direction). The laminate, though, is loaded in its own x-y axes. So each ply's stiffness matrix is rotated from material coordinates into laminate coordinates through its angle. Two identical plies at 0 and 45 degrees contribute completely different stiffness to the same laminate.

The stack becomes the ABD matrix

Sum the rotated plies through the thickness and you get one 6x6 matrix relating the forces and moments you apply to the strains and curvatures you get. It splits into three blocks:

• [A] - extensional: in-plane force to in-plane strain. How stiff the laminate is when you pull on it.
• [B] - coupling: pull on it and it bends. Zero for symmetric laminates, which is why symmetry is the default in practice.
• [D] - bending: moment to curvature. Weighted by the cube of distance from the midplane, so plies on the outside dominate.

That z-cubed weighting in [D] is the single most useful thing to internalise: where a ply sits matters as much as how many of them you have. The default layup on this page is quasi-isotropic in plane, E_x = E_y = 60.5 GPa, and yet its bending stiffness is E_fx = 96.8 GPa against E_fy = 29.7 GPa, purely because the 0 degree plies happen to be on the outside.

Invert it for engineering constants

Engineers rarely want raw stiffness terms; they want moduli they can compare to a datasheet. Inverting [A] gives the membrane constants E_x, E_y, G_xy, v_xy, and inverting [D] gives the flexural set E_fx, E_fy, G_fxy. Both are on screen behind the engineering constants toggle.

Know where it stops

CLT is exact within its assumptions, not an approximation - but the assumptions are real limits. Thick laminates need shear deformation theory, and free edges, holes, bolted joints and ply drops need 3D analysis, because that is where interlaminar stresses drive delamination and CLT cannot see them.