# Visualize the variation of engineering constants for an angle-ply based on those for a unidirectional lamina and the angle of the ply using Matlab

## Summary

In this assignment students will use the provided Matlab functions to create the plots showing the variation of engineering properties with respect to the fiber angle theta for graphite-reinforced composites.

## Learning Goals

Students will gain a deeper understanding of the behavior of orthotropic materials.
Students will learn how the engineering constants vary with respect to the angle of the ply for a unidirectional angle-ply.
Students will learn data plotting in Matlab.
Students will learn how to use Matlab functions in their scripts.
Students will learn simple programing tricks in Matlab.
Matlab is used to 1) create the plots and, 2) create functions incorporating the formulations for the engineering constants of an orthotropic material.
The students will gain higher-order thinking skills by learning how to make sense of of the mathematical formulations through data visualization.
Students will develop better programming skills in this activity.

## Context for Use

Educational level: college upper level, class size: 10-30 students
Institution type: university or college
Type of activity: lab activity in a classroom
Level of skills: students are required to have basic knowledge of graphing and programing with Matlab
Other required skills: the basic knowledge of strength of materials
This activity is part of the hands-on learning of mechanics of composite materials. This activity could be easily adapted in other educational settings where there is a need for data visualization and interpretation.

## Description and Teaching Materials

In this activity, students are first introduced to the basic concepts of macromechanics of orthotropic materials. Then, they are asked to study the case of an angle-ply lamina, more specifically, how the engineering properties such as the elastic moduli, the shear modulus and the Poisson's rations vary with the ply angle. Students are provided with the materials properties as well as the Matlab functions incorporating the mathematical formulations for the engineering constants and are asked to create the plots visualizing their variations against the ply angle. Students are then required to interpret the graphs.
Handout (Acrobat (PDF) 260kB Sep14 21)

Matlab functions needed for this hands-on activity. (Zip Archive 182.1MB Sep14 21)

## Teaching Notes and Tips

Quick notes regarding using Matlab:
Students may not know how to 1) incorporate a function into their scrip, and 2) create a plot using an existing Matlab function that generates scalar outputs only. This assignment shows them how to do that.

## Assessment

The outputs are the Matlab figures. If they match those of the problem statement, they will get the full credit, if not they will get partial credit depending on the accuracy of the results.

## References and Resources

https://extras.springer.com/2005/978-3-540-24353-3.zip