Variationally correct assumed strain field for the simple curved beam element

The classical curved beam element (the cubic-linear element) has been discredited for a long time because of poor performance. In a previous paper, the first author showed that the poor performance could be attributed to the inconsistency in the membrane strain field interpolations and that this could be improved by designing a new membrane strain field which met the consistency requirements. This paper shows that this formulation can be improved by re-constituting the 'assumed' strain field in a variationally correct manner