A laminate stiffness follows the rule of mixtures for its fibers and matrix, then classical beam theory relates load to bending deflection and ply-by-ply stress.
E_composite = Vf·E_fiber + (1−Vf)·E_matrix
δ = F·L³ / (3·E·I), σ(y) = M·y / I
- Tip load — force applied at the free end of the cantilever laminate.
- Fiber volume fraction — proportion of stiff fiber vs. softer matrix, raising modulus as it increases.
- Layup angle — fiber orientation relative to the load axis; off-axis plies carry less bending stress.
- Material — carbon fiber (highest stiffness/weight), glass fiber (cheaper, more flexible), or ceramic matrix (very stiff, brittle, heat-resistant).
Real-world use: aerospace wing spars and automotive chassis panels use exactly this fiber/matrix/layup trade-off to hit stiffness-to-weight targets.