Note that the shape functions of eqns. (9.89) are linear in x and y. Further, evaluation of eqns. (9.89) shows that shape function Nt(xj, y, ) = 1 and N,(x, y) — 0 at nodes j and k, and at all points on the line joining these nodes. Similarly, Nj(xj, yj) — 1 and Nk(xk, yk) = 1, and equal zero at, and on the line between, the other nodes.

Formulation of element stiffness matrix

For plane stress analysis, the strain/displacement relations are exx = du/dx, £ Vv = dv/dy, exy — du/dy + dv/dx where exx and £vv are the direct strains parallel to the x and y axes, respectively, and exy is the shear strain in the xy plane. Writing in matrix form gives



d/dx o 0 d/dy L d/dy d/dxJ
0 0

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