Solid Mechanics Problems - Meshless Methods in Biomechanics - page 185

Fig. 5.32 Medium
displacement errors obtained
for the: a regular nodal
distribution; b irregular nodal
distribution. Logarithmic
scales

(a)

(b)

The analytical displacement field [ 15 ] is obtained from the analytical stress field
on Eq. ( 5.11 ).

y

3x ð 2L x Þ y þð 2 þ t Þ y 2 D 2
4

u ð x Þ ¼ 2P
E D 3

ð 5 : 12 Þ

v ð x Þ ¼ 2P
E D 3

x 2 ð 3L x Þþ 3t ð L x Þ y 2 þ x ð 4 þ 5t Þ D 2
4

The problem was studied considering the two-dimensional analysis and also the
three-dimensional analysis. Several regular and irregular nodal meshes, increas-
ingly denser, were used to discretize the solid domain. In Fig. 5.37 two-dimen-
sional and three-dimensional nodal discretizations examples are presented. As in
previous example, in order to preserve a well-balance three-dimensional nodal