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, 2D Hoffman, Tsai-Wu, Azzi-Tsai-Hill and Maximum Strain)
• Evaluation of stress-based damage initiation criteria (Hashin's Theory and LaRC05)
• Support for user-defined failure criteria
• 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

Methodology

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)

Getting started

The main analysis function is called as follows:

[<output-structure>] = abd.main(<input-structure>);

Detailed information about defining <input-structure> is found in the help text located inside lat.m:

help lat

The following template file automatically generates the input structure based on the supplied user definitions. Simply fill out the options, then select Run or hit F5 to start the analysis:

edit user_definitions.m

Output

The output of the analysis is located under output\<job-name>.

Analysis summary file:

summary.log

Output variable file:

output.mat

Job settings record file:

settings.mat

The job settings record file can be used as input to the main analysis function:

[..] = abd.main('settings.mat');

Creating user-defined failure criteria

Generate a template routine file for the user-defined failure criterion:

abd.createUcrt('<criterion-name>')

Specify the user-define criterion in the user definition file:

OUTPUT_STRENGTH = {@<criterion-name>, {'RESERVE' | 'VALUE'}};

Example template routine file containing a user-defined failure criterion:

edit ucrt_example.m

Files

Main analysis function:

+abd/main.m

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

validation/validate_hashin.m
validation/validate_abaqus.m
validation/validate_joyce.m

Abaqus input files for validation:

validation/hashin_abaqus.inp
validation/uniaxial_abaqus.inp

Internal functions for calculation:

+abd/internal_<fun>.m

Documentation

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

help lat

Example Layup Analysis Tool analyses:

edit examples.m

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)