肉黑功=偶+r+妈5 △公A (a) (b) 阁 倒3 nddee间6 ode业同i0oese =女b-+-n+n- Area Coordina 套誉 Li+L+L= Mn-与-h+-约+对-时 A 北剑 ix-Node Triangular Element 卧：目 -(L- 月-可目 -(-)-- 自3 Triangular elements For each element, how to express the field variable in the polynomial form? Results? (a) 3-node linear, (b) 6-node quadratic, (c) 10-node cubic. A general three node triangular element referred to global coordinates. Assumed: each node 1 DOF                                      3 2 1 2 1 0 3 3 2 2 1 1 3 3 3 2 2 2 1 1 1 0 1 2 1 1 1 ( , ) ( , ) ( , ) ( , )           a a a x y x y x y x y x y x y x y a a x a y Area Coordinates Areas used to define area coordinates for a triangular element. (a) Area A1 associated with either P or P is constant. (b) Lines of the constant area coordinate L1. When expressed in Cartesian coordinates, the interpolation functions for the triangular element are algebraically complex. Further, the integrations required to obtain element characteristic matrices are cumbersome. Considerable simplification of the interpolation functions as well as the subsequently required integration is obtained via the use of area coordinates. Six-Node Triangular Element (a) Node numbering convention. (b) Lines of constant values of the area coordinates. RECTANGULAR ELEMENTS (a) the translation to natural coordinates, (b) the natural coordinates of each node. A four-node rectangular element defined in global coordinates