Stacking Sequence Bending Stiffness Calculator

Stacking Sequence & Bending Stiffness

The bending stiffness (D matrix) of composite laminates is highly dependent on ply stacking sequence. This calculator uses the **correct cubic formula** for symmetric laminates, eliminating warpage and coupling effects.

Correct Formula (Classical Laminate Theory)

Where:
• D_ij = Bending stiffness components (N·mm)
• Q_ij = Transformed reduced stiffness matrix
• z = Distance from laminate midplane (mm)
• θ_k = Ply angle of k-th layer
Note: Input the half layup sequence (calculator automatically generates symmetric laminate [layup]s)

Input Parameters (Symmetric Layup)

Longitudinal Modulus E₁ (MPa) Transverse Modulus E₂ (MPa) Shear Modulus G₁₂ (MPa) Poisson's Ratio ν₁₂ Single Ply Thickness (mm) Half Layup Sequence (e.g. 0,45,-45,90 → [0/45/-45/90]s) Calculate Bending Stiffness

Typical Real-World Example (T700/Epoxy)

Symmetric Laminate [0/45/-45/90]s (8 layers, t=0.125mm, total thickness=1.0mm):
D₁₁ ≈ 7996 N·mm, D₂₂ ≈ 2054 N·mm, D₁₂ ≈ 1237 N·mm, D₆₆ ≈ 1428 N·mm
This matches typical engineering ranges for aerospace-grade composites.

Key Engineering Notes

• 0° plies on the outer surface maximize bending stiffness (D₁₁ > D₂₂)
• Symmetric layup eliminates warpage and B matrix coupling (industry standard)
• Input sequence is the half layup (calculator automatically mirrors for symmetry)
• Use cubic formula only (square terms in formulas are incorrect for bending stiffness)