Inflectional Heavy Elastica with Unilateral Contact constraint: Analytical Solution through the Curvilinear Abscissa Mapping approximation

This paper provides an original approximate analytical solution of the Inflectional Heavy Elastica problem using the Curvilinear Abscissa Mapping Method (C.A.M.M.). The solution, unlike the classic approximate methods, is valid for a wide range of rotations (up to 90 degrees). As well known, the Heavy Elastica (inflectional or not) does not have an exact solution, even in the simplest load cases. CAMM approach allows to obtain an approximate analytical solution that even sounds for very large displacements and rotations. In the present contribute we refer to the inflectional case, which subsists when the orientation of the end-moment acts against the bending due to the lifting load. The proposed solution has a similar mathematical form and computational effort required for the classical non-inflectional Elastica (non-distributed loads). The results are validated by some numerical and experimental comparisons, highlighting a strong matching. Design-Charts are also provided, in which the vari-ables of interest are deducible upon the trend of dimensionless parameters, as function of end rotation or end-applied moment.