AENGM0009 Research Development

AENGM0012 Research Skills

Matlab Assignment

Submission: 27 November 2015, 4pm

Alberto Pirrera and Matt O’Donnell

x

y

z

a

b

q(x,y)

Figure 1: Thin plate subjected to uniform load.

Assignment

Consider the plate in figure 1, which is simply supported along all four edges,subjected to a ramp load q(x, y) = q0

xa and made of an antisymmetric stacking

sequence.Its transverse displacement field, w0, can be found as a Navier-type solution

of the governing equation

D11∂4w0

∂x4+ 2(D12 + 2D66)

∂4w0

∂x2∂y2+D22

∂4w0

∂y4= q.

In particular, it can be shown that

w0 =

∞∑n=1

∞∑m=1

Qmn

dmnsin

mπx

asin

nπy

b,

where

Qmn = −8q0π2

(−1)m

mnm = 1, 2, 3, . . . n = 1, 3, 5, . . .

and

dmn =π4

b4

[D11m

4 b4

a4+ 2(D12 + 2D66)m2n2

b2

a2+D22n

4

].

You are tasked with writing the following Matlab routines:

1

1. A function to calculate the Classic Laminate Theory stiffness matricesA, B, D (for generic laminates).

2. A function to calculate the location and maximum value of w0 for arbi-trary a, b and q0.

3. Using these functions, write a script to produce a convergence diagramof the maximum value of w0 as a function of n and m.

Assessment

Accuracy of your code will be assessed via a Blackboard page, where youwill be asked to provide the results from the analysis of a specific system (i.e.dimensions, material properties, stacking sequence, loading, etc., will be given).This will be a pass/fail assessment, however you will have unlimited attemptsto validate your code.

The functions are to be written in the style of Matlab’s built-in functions,resembling a subroutine that is callable from an independent program. Thismeans providing clear inputs and outputs, together with internal documentationon how to use the code, e.g. comments and docstrings.

You will also be expected to provide short user guides for the two functions.You are permitted up to four pages in total. The guides should be in the styleof the Matlab’s Help documents (See for instance fzero1), including examplesof usage and references to relevant literature. No user guide is required for thescript.

All codes and user guide must be submitted via the Blackboard submissionpoint: ‘B1 Matlab Exercise Submission Point’.

Finally, you will be asked to demonstrate and discuss your code and userguides in an oral examination. Here, you will be assessed on the clarity, structureand style of your code, together with your understanding of the principles ofprogramming and Matlab code vectorisation.

Assessment will be based on the following weightings:

• User guide - clarity and completeness 40%

• Code - ease of use 10%

• Code - style/use of comments 20%

• Code - data/program structure and code vectorisation 30%

N.B. There will be a penalty for codes that fail to pass the Blackboardaccuracy test. The penalty will be determined by your ability to explain yourdebugging approach during the oral examination. Penalties will be up to 50%of the overall mark.

Optional code development

Using Matlab’s Genetic Algorithm implementation to search for the anti-symmetric stacking sequence consisting of 10 plies that minimises the maximumvalue of w0. You can then compare your results with an exhaustive search tocheck that the Genetic Algorithm has found the global optimum.

1http://uk.mathworks.com/help/matlab/ref/fzero.html?searchHighlight=fzero

2