# Laminate Stiffness

> Use when you must compute the stiffness of a composite laminate with classical lamination theory: build the ply stiffness from the material constants, rotate it to the ply angle, and assemble the A matrix for a symmetric laminate. Produces the ply stiffness, the rotated stiffness with coupling terms, and the laminate A matrix used in strength and stability analyses. Trigger: composite laminate, classical lamination theory, ply stiffness, laminate a matrix, symmetric laminate, composites.

- Skill: `ashfordeou/laminate-stiffness` (Agent Skill, multi-file: 3 files)
- Install (CLI): `npx skillmds@latest add ashfordeou/laminate-stiffness`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/laminate-stiffness/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: Apache-2.0
- Author: ashfordeOU (https://skillmd.com/u/ashfordeou)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ashfordeou/laminate-stiffness

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# Composite Laminate Stiffness (structures/composites/laminate-stiffness)

Use when the task is composite laminate stiffness with classical
lamination theory: ply stiffness, rotation, and the symmetric
laminate A matrix.

## Domain quick reference

- A ply has orthotropic stiffness in material axes: Q11, Q12,
  Q22, Q66 from the engineering constants.
- Rotation to the laminate axes produces Q-bar; the coupling terms
  Q16 and Q26 vanish for 0 and 90 degree plies.
- The laminate A matrix sums Q-bar times ply thickness; for a
  balanced symmetric laminate the A16 and A26 terms vanish.
- Composite airframe practice sits in the FAR-25 / CS-25
  certification context for transport aeroplanes.

## Workflow

1. Collect ply engineering constants E1, E2, nu12, G12.
2. Build the material stiffness with ply_stiffness.
3. Rotate each ply with rotated_ply_stiffness.
4. Assemble the A matrix with laminate_a_matrix.
5. Confirm the coupling terms are small for symmetric balanced
   laminates.

## Pitfalls

- Forgetting nu21 = nu12 * E2 / E1 in the denominator.
- Assembling an unsymmetric stack and reading coupling terms as
  zero.
- Mixing degrees and radians in the rotation.

## Behavior contract (gate 3)

The ply, rotation, and A matrix logic is exercised by the gate 3
contract test: scripts/test_laminate_stiffness.py against
scripts/laminate_stiffness_logic.py (stdlib unittest, offline).
Run:
python3 scripts/test_laminate_stiffness.py

## Compliance

- Standards referenced, not reproduced: FAR-25 is US government
  work (public domain) and CS-25 is a free EASA download; the CLT
  math is common mechanics, summary-only per standards-map.yaml.
- compliance: STANDARDS-REF, gated: false.