A simplified approach to solve quasi-statically moving load problems of elastica using end loaded elastica solution

Elastica problems with non-conservative moving forces are more complicated as compared to end loaded elastica problems. Established methods exist to solve an end loaded elastica problem. For solving a moving boundary problem, such methods need considerable modification or re-formulation. In this article, results of an end loaded elastica problem which is readily obtainable are used to solve two relatively involved moving boundary cases. The solution methodology involves a unique normalization procedure for the available elastic solution followed by few simple steps. One of the problems considered is three point bending of elastica with finite roller dimension. The other one being cantilever elastica under the action of wedge contact. Structural stiffening is observed in both the cases as a result of moving boundary condition as compared to when roller dimension is negligible or wedge makes only point contact. A structured approach may potentially originate from this kind of procedure to tackle more complicated moving boundary problems of elastica.