  This letter aims at resolving the issues raised in the recent short
communication [1] and answered by [2] by proposing a systematic approximation
scheme based on non-mapped shape functions, which both allows to fully exploit
the unique advantages of the smoothed finite element method (SFEM) [3, 4, 5, 6,
7, 8, 9] and resolve the existence, linearity and positivity deficiencies
pointed out in [1]. We show that Wachspress interpolants [10] computed in the
physical coordinate system are very well suited to the SFEM, especially when
elements are heavily distorted (obtuse interior angles). The proposed
approximation leads to results which are almost identical to those of the SFEM
initially proposed in [3]. These results that the proposed approximation scheme
forms a strong and rigorous basis for construction of smoothed finite element
methods.
