Heavy Elastica soil-supported with lifting load and bending moment applied to an end: A new analytical approach for very large displacements and experimental validation

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

“…Considering a reference system aligned with the unloaded rectilinear beam, the governing equations for the Heavy Elastica problem are [21]:…”

“…In other words, it will be clear hereinafter that the differential equation that derives by equilibrium, although simple, does not allow being integrated in its actual form. For an extensive review on analytical methods to obtain approximate analytical solutions and on the reasons for their limitations and/or inadequacies, refer to [21,34,36].…”

“…This approach (without the mention of its name) was first proposed by [12] in a simplified form, which allows reliable solutions only for moderate displacements and rotations. In [21], the method has been refined and discussed to apply even for very large displacements and rotations of non-inflectional Heavy Elastica, supported by soil. In the present paper, we encompass occurrence of an internal inflection point (this happens when reversing the sign of the ending-moment).…”

“…In the present paper, we encompass occurrence of an internal inflection point (this happens when reversing the sign of the ending-moment). The starting-point is the same as [21], namely the assumption of parabolic mapping between curvilinear and Cartesian abscissae. The inflection occurrence implies that the three intersection points of the parabolic mapping are chosen in a non-fixed location as in the noninflectional case [21].…”

“…The starting-point is the same as [21], namely the assumption of parabolic mapping between curvilinear and Cartesian abscissae. The inflection occurrence implies that the three intersection points of the parabolic mapping are chosen in a non-fixed location as in the noninflectional case [21]. Furthermore, in this case there are two additional boundary conditions and two additional kinematic unknowns.…”