ABSTRACT
This equation is formally the same as for a rod equation (see Equation 9.1), furnishing the interpolation model for the element as
(9.11)
9.1.2 INTERPOLATION MODELS: TWO DIMENSIONS
9.1.2.1 Membrane Plate
Now suppose that the displacements u(x, y, t) and v(x, y, t) are modeled on the triangular plate element in Figure 9.3, using the values ue(t), ve(t), ue+1(t), ve+1(t), ue+2(t), and ve+2(t). This element arises in plane stress and plane strain, and is called a membrane plate element. A linear model suffices for each quantity because it provides three coefficients to match three nodal values. The interpolation model now is
9.1.2.2 Plate with Bending Stresses
In a plate element experiencing bending only, the in-plane displacements, u and v, are expressed by
(9.13)
in which z=0 at the middle plane. The out-of-plane displacement, w, is assumed to be a function of x and y only.
