A quintic polynomial series is adopted for the transverse displacement function

(18.11)

where,

(18.12)

By using Equation (18.7), each elements of U can be expressed in terms of the elements of C. There are ten such relations corresponding to the ten in-plane DOF which can be summarized as a matrix equation.

(18.13)

The constants of the in-plane displacement polynomial can be expressed in terms of U as

(18.14)

where

(18.15)

However, using this relation, the in-plane displacement field u can be expressed in terms of nodal DOF U as

(18.16)

Similarly,

(18.17)

and

(18.18)

where,              

and

(18.19)

 and   are the transformation matrices between natural and global coordinates.