User:Eas4200c.f08.carbon.orear/HW6/Composites

Composite Laminate Analysis: MATLAB Code Study
The code below, developed by carbon.orear and carbon.clausen, is used to analyze stress and strain in a composite laminate. This material is relevant to this course and is presented in Chapter 8 of the Sun book. It has been added to this Homework as an additional contribution and so that students may get an understanding of this material beyond the scope of this course. The material covered in Chapter 8 is extensive and it is uncertain at this time whether much of this course will focus on it.

For additional information, students can enroll in Dr. Ifju's Aerospace Structural Composites Course offered in Spring 2009.

This code is extensive, but has been slightly commented for ease of understanding. Most of the outputs are not cohesive without reading the comments in the code. Plots generated must be connected by hand as seen in the second example plot.

The Test Case is Example 8.4. from pg. 288 in the Sun book.

Case Test
EXAMPLE 8.4 in the Sun book has been used as a test model. A known strain input was given instead of a known Nx.

EDU>> layers

How many layers are there? 8

What is the thickness of each layer? .127/1000

What is the value of E (in GPa) in the (1) direction? 140

What is the value of E (in GPa) in the (2) direction? 10

What is the value (in GPa) of G12? 7

What is the value of the Poisson ratio in the (12) direction? .3

For the given properties the number of layers and Q matrix is given: 8

Q =

1.4091e+002 3.0194e+000            0 3.0194e+000 1.0065e+001            0 0           0  7.0000e+000

-5.0800e-004 -3.8100e-004 -2.5400e-004 -1.2700e-004 0 1.2700e-004 2.5400e-004 3.8100e-004 5.0800e-004

layer 1

What is the fiber orientation for this layer in radians? pi/4

layer 2

What is the fiber orientation for this layer in radians? -pi/4

layer 3

What is the fiber orientation for this layer in radians? 0

layer 4

What is the fiber orientation for this layer in radians? pi/2

layer 5

What is the fiber orientation for this layer in radians? pi/2

layer 6

What is the fiber orientation for this layer in radians? 0

layer 7

What is the fiber orientation for this layer in radians? -pi/4

layer 8

What is the fiber orientation for this layer in radians? pi/4

7.8540e-001 -7.8540e-001 0 1.5708e+000 1.5708e+000 0 -7.8540e-001 7.8540e-001

(:,:,1) =

4.6252e+001 3.2252e+001  3.2710e+001 3.2252e+001 4.6252e+001  3.2710e+001 3.2710e+001 3.2710e+001  3.6233e+001

(:,:,2) =

4.6252e+001 3.2252e+001 -3.2710e+001 3.2252e+001 4.6252e+001 -3.2710e+001 -3.2710e+001 -3.2710e+001 3.6233e+001

(:,:,3) =

1.4091e+002 3.0194e+000            0 3.0194e+000 1.0065e+001            0 0           0  7.0000e+000

(:,:,4) =

1.0065e+001 3.0194e+000  4.2585e-016 3.0194e+000 1.4091e+002  7.5859e-015 4.2585e-016 7.5859e-015  7.0000e+000

(:,:,5) =

1.0065e+001 3.0194e+000  4.2585e-016 3.0194e+000 1.4091e+002  7.5859e-015 4.2585e-016 7.5859e-015  7.0000e+000

(:,:,6) =

1.4091e+002 3.0194e+000            0 3.0194e+000 1.0065e+001            0 0           0  7.0000e+000

(:,:,7) =

4.6252e+001 3.2252e+001 -3.2710e+001 3.2252e+001 4.6252e+001 -3.2710e+001 -3.2710e+001 -3.2710e+001 3.6233e+001

(:,:,8) =

4.6252e+001 3.2252e+001  3.2710e+001 3.2252e+001 4.6252e+001  3.2710e+001 3.2710e+001 3.2710e+001  3.6233e+001

ABD info 6.1843e-002 1.7918e-002            0 1.7918e-002 6.1843e-002  1.7347e-018 0 1.7347e-018  2.1962e-002

0           0            0            0            0            0            0            0 -4.2352e-022

4.8977e-009 2.4994e-009  8.0404e-010 2.4994e-009 3.8257e-009  8.0404e-010 8.0404e-010 8.0404e-010  2.8473e-009

ans =

1.7652e+001 -5.1144e+000 4.0397e-016 -5.5026e-030 -9.9505e-030  6.4451e-029 -5.1144e+000 1.7652e+001 -1.3943e-015  1.8992e-029  3.4343e-029 -2.2245e-028 4.0397e-016 -1.3943e-015 4.5533e+001 -6.2022e-013 -1.1216e-012  7.2645e-012 -5.5026e-030 1.8992e-029 -6.2022e-013  3.0904e+008 -1.9515e+008 -3.2163e+007 -9.9505e-030 3.4343e-029 -1.1216e-012 -1.9515e+008  4.0111e+008 -5.8161e+007 6.4451e-029 -2.2245e-028 7.2645e-012 -3.2163e+007 -5.8161e+007  3.7671e+008

Input the midplane strains in a vector of the form [x y xy]. [1000e-6 0 0]

midstrains =

1.0000e-003           0            0

Input the midplane curvatures (in m^-1) in a vector of the form [x y xy]. [0 0 0]

midcurvs =

0    0     0

1.0000e-003 1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003 0           0            0            0            0            0            0            0            0            0            0            0            0            0            0            0

1.0000e-003 1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003 0           0            0            0            0            0            0            0            0            0            0            0            0            0            0            0

4.6252e-002 4.6252e-002  1.4091e-001  1.0065e-002  1.0065e-002  1.4091e-001  4.6252e-002  4.6252e-002 3.2252e-002 3.2252e-002  3.0194e-003  3.0194e-003  3.0194e-003  3.0194e-003  3.2252e-002  3.2252e-002 3.2710e-002 -3.2710e-002           0  4.2585e-019  4.2585e-019            0 -3.2710e-002  3.2710e-002

4.6252e-002 4.6252e-002  1.4091e-001  1.0065e-002  1.0065e-002  1.4091e-001  4.6252e-002  4.6252e-002 3.2252e-002 3.2252e-002  3.0194e-003  3.0194e-003  3.0194e-003  3.0194e-003  3.2252e-002  3.2252e-002 3.2710e-002 -3.2710e-002           0  4.2585e-019  4.2585e-019            0 -3.2710e-002  3.2710e-002

1.5000e-003 5.0000e-004  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  5.0000e-004  1.5000e-003 5.0000e-004 1.5000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.5000e-003  5.0000e-004 1.1102e-019 1.1102e-019  5.0000e-004 -5.0000e-004 -5.0000e-004  5.0000e-004  1.1102e-019  1.1102e-019

1.5000e-003 5.0000e-004  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  5.0000e-004  1.5000e-003 5.0000e-004 1.5000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.0000e-003  1.5000e-003  5.0000e-004 1.1102e-019 1.1102e-019  5.0000e-004 -5.0000e-004 -5.0000e-004  5.0000e-004  1.1102e-019  1.1102e-019

7.1963e-002 7.1963e-002  1.4091e-001  3.0194e-003  3.0194e-003  1.4091e-001  7.1963e-002  7.1963e-002 6.5421e-003 6.5421e-003  3.0194e-003  1.0065e-002  1.0065e-002  3.0194e-003  6.5421e-003  6.5421e-003 -7.0000e-003 7.0000e-003            0 -8.5725e-019 -8.5725e-019            0  7.0000e-003 -7.0000e-003

7.1963e-002 7.1963e-002  1.4091e-001  3.0194e-003  3.0194e-003  1.4091e-001  7.1963e-002  7.1963e-002 6.5421e-003 6.5421e-003  3.0194e-003  1.0065e-002  1.0065e-002  3.0194e-003  6.5421e-003  6.5421e-003 -7.0000e-003 7.0000e-003            0 -8.5725e-019 -8.5725e-019            0  7.0000e-003 -7.0000e-003