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!

Fig: 1