EN0175-15

# EN0175-15 - EN0175 10 24 06 Review of deformation tensors F...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EN0175 10 / 24 / 06 Review of deformation tensors: F , C , B , U , V , R , E , * E Given F , one can follow the following standard procedure to determine the other strain measures. 1) Most simply, F F C T = , T F F B = , ( ) I C E − = 2 1 , ( ) 1 * 2 1 − − = B I E 2) To fine U , V , R , we need to perform the eigenvalue analysis of C and B (diagonalization of matrices): III III III II II II I I I III II I m m m m m m C m m C v v v v v v v v ⊗ + ⊗ + ⊗ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⇒ = 2 2 2 2 2 2 2 λ λ λ λ λ λ λ III III III II II II I I I III II I n n n n n n B n n B v v v v v v v v ⊗ + ⊗ + ⊗ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⇒ = 2 2 2 2 2 2 2 λ λ λ λ λ λ λ 3) III III III II II II I I I m m m m m m U v v v v v v ⊗ + ⊗ + ⊗ = λ λ λ III III III II II II I I I n n n n n n V v v v v v v ⊗ + ⊗ + ⊗ = λ λ λ j i ij e U e U v v ⋅ = , j i ij e V e V v v ⋅ = ⇒ U and V 4) R V U R F = = F V U F R 1 1 − − = = Generalized Hooke’s law...
View Full Document

## This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

### Page1 / 6

EN0175-15 - EN0175 10 24 06 Review of deformation tensors F...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online