A hypergeometric treatment to explain the nonlinear true behavior of redundant constraints on a straight elastic rod
arXiv:1505.02255
Abstract
In theory and practice of elastic straight rods, the statically indeterminate reactions acted by perfect constraints are commonly believed not to depend on the flexural stiffness . We solve exactly two elastica problems in order to obtain hypergeometrically (helped by Lagrange, Lauricella, Appell), the true displacements upon which the forces method is founded. As a consequence, the above reactions are found to depend on stiffness: the presumptive independence credited as general, is far from being always true, but, quite the contrary, is valid only within a first-order approximation.
13 pages, 8 figures