
Convergence and consistency analyses 175
The beam parameters are q = −3.0N, E = 3 × 10
7
Pa, v
0
= 0.3, length(L) =
20m, thickness(t) = 0.1m, and width(D) = 1.0m. The analytical solutions
of the deection and slope are, respectively,
wx
qx Lx
EI
dw x
dx
q
EI
xL Lx x
()
()
24
,and
()
12
22
223
=
−
=
(4.57)
The problem is solved by the 41 uniform and random eld nodes separately
combined with the 41 cosine virtual nodes. The numerical solutions are
plotted in Figure4.23, and the numerical results match almost exactly with
the corresponding analytical values. The nonlinear electrostatic force eld
is then applied on the xed–xed beam as
qx ...