114
J. Chen et al.
z
α 1 =
ϕ
=
2
α
Indicator
Fixed
Fixed
Fig. 17. Model and mesh for the spiral cylindrical shell
Table 7. w for the spiral cylindrical shell
4 × 4 8 × 8 16 × 16
SEIA
6.8975 8.2547 8.4932
Reference [32] 8.5091
5 Concluding Discussions
A new locking-free thick/thin shell element, the SEIA, is proposed in this paper. To
summarize the development methodology, an incompatible polynomial displacement
approximation is defined in each independent polygonal element, and fictitious thin
layers are introduced to enforce the displacement conformity between adjacent elements.
The methodology is inspirational for the construction of locking-free thick/thin shell
elements.
As seen from the numerical investigations and comparisons, the SEIA exhibits the
following characteristics.
1) The third order polynomial is used for the displacement approximation, which avoids
the shear and membrane locking naturally when applied to thin shells in engineering.
Hence, the SEIA can be used for the analysis of the thick/thin shell, and the problems
introduced by numerical expediencies are prevented.
2) Fictitious thin layers are introduced to enforce the displacement conformity between
adjacent elements. In consequence, the SEIA has simpler theoretical derivation
J. Chen et al.
z
α 1 =
ϕ
=
2
α
Indicator
Fixed
Fixed
Fig. 17. Model and mesh for the spiral cylindrical shell
Table 7. w for the spiral cylindrical shell
4 × 4 8 × 8 16 × 16
SEIA
6.8975 8.2547 8.4932
Reference [32] 8.5091
5 Concluding Discussions
A new locking-free thick/thin shell element, the SEIA, is proposed in this paper. To
summarize the development methodology, an incompatible polynomial displacement
approximation is defined in each independent polygonal element, and fictitious thin
layers are introduced to enforce the displacement conformity between adjacent elements.
The methodology is inspirational for the construction of locking-free thick/thin shell
elements.
As seen from the numerical investigations and comparisons, the SEIA exhibits the
following characteristics.
1) The third order polynomial is used for the displacement approximation, which avoids
the shear and membrane locking naturally when applied to thin shells in engineering.
Hence, the SEIA can be used for the analysis of the thick/thin shell, and the problems
introduced by numerical expediencies are prevented.
2) Fictitious thin layers are introduced to enforce the displacement conformity between
adjacent elements. In consequence, the SEIA has simpler theoretical derivation