# MSQ3 - 3 Layer Upon Layer Upon Layer A Determining Angle...

This preview shows pages 1–5. Sign up to view the full content.

3 Layer Upon Layer Upon Layer! A] Determining Angle α Assumptions Hookean ( = E σε ) Orthotropic (Makes matrix nicer, stress smearing, more on this in part B) Symmetry (looks like it is, and it has to be, more on this in part C) Solution Approach Values are given for principle direction variables, which I will use with the equations below to work towards and eventually setting equal to the testing moduli of the whole (all layers) annulus fibrosus. Following along my train of thought should be clear, and my motives behind what I calculate should be evident. Equations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
I must break this down into “Front Layer” and “2 nd Layer.” At the very end I will take into account that there are 5 “front layers” and 5 “2 nd layers,” but to get to that point I must start with single 2-D layers. Also, for sake of not having messy subscripts (you’ll see further on), instead of referring to the 2 nd layer as “2 nd layer”, from this point on I will refer to it as “back layer,” even though I know the true back layer is actually the same as the front layer.
Front Layer Known = E1 120 MPa = E2 20 MPa =. ν12 4 = =. ν21 ν12E2E1 067 = . = . G12 E22 6 7 69 Solving for Q's = - = . Q11 E11 ν12ν21 123 31 = - = = . Q12 ν12E21 ν12ν21 Q21 8 22 = - = . Q22 E21 ν12ν21 20 55 = = . Q66 G12 7 69 = . ( ( )) + . + * . ( ( )) ( ( )) + . ( ( )) Q11 123 31 cos α 4 28 22 2 7 69 sin α 2 cos α 2 20 55 sin α 4 = . + . + * . ( ( )) ( ( )) + . ( +( ( )) ) Q12 123 31 20 55 4 7 69 sin α 2 cos α 2 8 22 sinα4 cos α 4 = . ( ( )) + . + * . ( ( )) ( ( )) + . ( ( )) Q22 123 31 sin α 4 28 22 2 7 69 sin α 2 cos α 2 20 55 cos α 4 = . - . - * . ( ( )) + . - . + * . ( ( )) ( ) Q16 123 31 8 22 2 7 69sinα cos α 3 8 22 20 55 2 7 69 sin α 3 cosα

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
= . - . - * . ( ( )) +( . - . + * . ) ( ( )) Q26 123 31 8 22 2 7 69 sin α 3cosα 8 22 20 55 2 7 69 sinα cos α 3 =( . + . - * . - * . )( ( )) ( ( )) + . ( +( ( )) ) Q66 123 31 20 55 2 8 22 2 7 69 sin α 2 cos α 2 7 69 sinα4 cos α 4 Back Layer Known Take note that the axis is the same, however E1 now equals the front side’s E2 due to its inversion (back layer is just a horizontally-flipped version of the front layer).
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern