The displacements u2 of point A calculated by the four kinds of
time-stepping algorithms for these four different nodes distributions
are depicted from Fig. 10–13. It can be obtained from the
figures that, with increasing the boundary nodes, exact the results.
Only 80 boundary nodes already can achieve similar accurate results
compared to the finite element methods (FEM) with 576
quadratic elements. The internal nodes have a little effect on the
precision of the computation, since the models with some internal
nodes only changing the results temperately. It also can be seen
that, the effectiveness of these three in four kinds of time-stepping
algorithms are almost similar. However, the Newmark's algorithm
with δ¼0.7, α¼0.5 may leads to a smaller amplitude of the displacements,
which may due to the bigger imported artificial
damping. For the sake of accuracy, the considered cantilever beam
model with 80 boundary nodes and 45 internal nodes will be
applied for the following analyzation