2 first strain computation 2d coords towards the end of lecture 15 i i

Question

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!