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Fig. 2. Coordinate system and parameters of a point on the middle surface
Fig. 3. Coordinate system and parameters of an arbitrary point
Supposing that h 1 , h 2 , r 1 and r 2 are the curvilinear parameters of the middle surface
of the shell, the curvilinear parameters at location α 3 on the normal of the shell in Fig. 3
can be written as follows:
h
α 3
1 = h 1 (1 + α 3 /r 1 ), h
α 3
2 = h 2 (1 + α 3 /r 2 ),
(7)
r
α 3
1 = r 1 (1 + α 3 /r 1 ), r
α 3
2 = r 2 (1 + α 3 /r 2 ).
(8)
3 Formulation of the SEIA
3.1 Incompatible Approximation in Each Element
Consider a linear elastic shell undergoing infinitesimal deformation. Figure 4 shows a
general orthogonal curvilinear coordinate system α 1 α 2 α 3 for the middle surface of a
shell, where α 1 and α 2 are the principal curvature line directions of the points on the
middle surface.
The middle surface of the shell is discretized into arbitrary polygonal elements in the
curvilinear coordinate system α 1 α 2 α 3 , as shown in Fig. 4. According to the well-known