102
J. Chen et al.
3.2 Enforcement of the Conformity Between Adjacent Elements
With the definition of the displacement approximation in Eq. (11), the deformation of two
adjacent shell elements e i and e k in Fig. 6 is completely discontinuous because elements
e i and e k have their own DOFs. However, the displacement on the share boundary of
the nonoverlapping shell elements e i and e k should be continuous. Here, a fictitious thin
layer e l is introduced to enforce the conformity on the share boundary of elements e i
and e k . The dimensions of the fictitious thin layer are the width d , the length l and the
thickness H , where d << l and d << H .
Fig. 6. Enforcement of the conformity between adjacent elements
Because d << l and d << H , the variation of the displacements along axes ¯
α 1 and
α 3 can be ignored compared to the displacement along axis ¯
α 2 . Therefore,
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
∂ ¯
u 1 /∂ ¯
α 1 ≈0
∂ ¯
u 2 /∂ ¯
α 1 ≈ 0
∂u 3 /∂ ¯
α 1 ≈ 0
∂ ¯
u 1 /∂α 3 ≈ 0
∂ ¯
u 2 /∂α 3 ≈ 0
∂u 3 /∂α 3 ≈ 0
(20)