2. First Strain Computation - 2D coords.

Towards the end of lecture 15 I introduce the matrix equation:

e = D Neue =

1

2A

0 Y31

0

Y23

0 X32 0

X13 0

LX32 Y23 X13 31 X21

Y12 0

X21

Y12

Uxl

Uyl

Ux2

Uy2

Ux3

Uy3

= Buº,

in which A is the area of the element (triangle - computable using a simpler matrix

expression given at the end of lecture 15), j = Xį — Xj, Yij = Yi - Yj,

or nodal coordinate differences for the element (i.e. x; is the x-coordinate of node

i), and a ucn is the c-axis (x or y) displacement of node n (n = 1, 2, or 3). For the

purposes of computing strain, the area and nodal coordinate differences are

always computed from the reference, or undeformed mesh (the ones above), and

the displacements are computed from the difference in coordinates from a

deformed mesh (such as the two below) and the reference mesh. Two deformed

meshes:

Basic2D Deformed.ucd

Adv2D_Deformed.ucd

So, with the mesh reader (step 1), you can read in the two meshes of each type

(Basic or Advanced), IGNORE the z-coordinate, compute the reference values (A, Xij,

Yij), determine the differences in position of the nodal coordinates between the

reference and deformed meshes, and compute strain for each element. This of

course is done one element at a time. LOOPS!