Solid Mechanics Problems - Meshless Methods in Biomechanics - page 191

Fig. 5.39 Medium normal
stress r XX errors obtained for
the: a regular nodal
distribution; b irregular nodal
distribution. Logarithmic
scales

(a)

(b)

P and h the angle between the ox axis and the line oP, as Fig. 5.46 shows. As in
previous example, for the three-dimensional analysis, it is assumed on all domain
boundaries r zx ¼ r yz ¼ r zz ¼ 0. The analytical displacement field is obtained from
the analytical stress field on Eq. ( 5.13 ),

cos ð h Þþ a 2 cos ð 3h Þ

1 t Þ r þ 2 a 2
r 2 r a 4

u ð x Þ ¼ r 0

ð 1 þ t Þ

E

2 r 3

sin ð h Þþ a 2 sin ð 3h Þ

v ð x Þ ¼ r 0

ð

1 þ t

Þ

t r ð 1 2 t Þ a 2
r 2 r a 4

E

2 r 3

ð 5 : 14 Þ