Layup Analysis Tool

Strength analysis and layup optimisation of unidirectional fibre-reinforced composites.

Preamble

There are already several decent tools for the analysis of composite layups available on the MATLAB File Exchange, so why add another?

Layup Analysis Tool is a comprehensive package which offers ABD matrix output, stress calculation, failure assessment and layup design optimisation within a convenient and simple-to-use file submission:

• Definition of n-ply layups with user-defined fibre orientations
• Support for user-defined orthotropic elastic material properties (per ply)
• Support for variable thickness plies
• Support for n evenly-distributed section points (per ply)
• Computation of the A, B and D matrices, and their inverse
• Computation of the equivalent extensional and bending moduli (symmetric layups)
• Stress and strain calculation in X-Y and ply coordinates, based on applied forces and moments
• Pretty MATLAB figures of through-thickness stresses and strains
• Inclusion of thermal and hydroscopic loads
• User-defined output locations: Face (top, middle, bottom), envelope or section point list
• Evaluation of stress and strain-based static failure criteria (Maximum Stress, Tsai-Hill, Tsai-Wu, Azzi-Tsai-Hill and Maximum Strain)
• Evaluation of stress-based damage initiation criteria based (Hashin's Theory and LaRC05)
• Stacking sequence optimiser: Find the stacking sequence which minimises a user-selected criterion based on an objective function (maximum or mean). The optimiser algorithm takes advantage of the Parallel Computing Toolbox

With all of the above functionality in one place, I hope this submission adds value to the current offering!

Summary

[varargout] = abd.main(varargin) analyses a user-defined composite layup.

To get started with a calculation, simply run the helper function:

user_definitions

The methodology used by Layup Analysis Tool follows classical lamination theory (CLT) and assumes that the laminate obeys the Kirchhoff Hypothesis:

1. Transverse shear is negligible (plane stress in each ply)
2. Displacements u and v (in the plane of the lamina) are assumed to be linear functions of the thickness coordinate z (no warping)

Files

Input file containing all of the required user definitions (run this script to perform the layup analysis):

user_definitions.m % <-- Configure and run this script!

Main analysis function (user is not required to run this function):

+abd/main.m

Validation cases to show that Layup Analysis Tool produces reliable output:

validation/validate_abaqus.m
validation/validate_joyce.m

Abaqus input file for validate_abaqus_uniaxial.m:

validation/validate_abaqus_uniaxial.inp

Internal functions for calculation (user should only run these functions for debugging purposes):

+abd/internal_<fun>.m

Documentation

For detailed instructions on the required inputs for Layup Analysis Tool, please consult the help text located inside abd.main:

help abd.main

Support

For questions, comments or suggestions, please contact the author: [e-mail].

Acknowledgements

Theory reference

• H. N. R. Wagner, Python code (GitHub link)
• Y. Jack Weitsman et al., Coefficient of hydroscopic expansion (ScienceDirect link)
• Abbott Aerospace Canada Ltf, Definition of laminate plate element behaviour (link)

Resources

• Interactive composite laminate calculator (link)
• Finding stiffness matrices A, B and D (eFunda link)