Geometrically non-linear analysis of inclined elastic rods subjected to self-weight

Abstract

The behavior of inclined slender elastic rods subjected to axial forces and distributed load is discussed in this paper. Mathematical models and numerical solutions are developed for small and large displacements. A double-hinged boundary condition is assumed and the analysis is carried out for different values of non-dimensional weight (distributed load) and angle of inclination. The mathematical formulation results from considering geometrical compatibility, equilibrium of forces and moments and constitutive relations. For large displacements, a set of six first order non-linear ordinary differential equations with boundary conditions prescribed at both ends is obtained. This two-point boundary value problem is numerically integrated using a three-parameter shooting method. When small displacements are assumed the problem simplifies and a power series solution may be conveniently employed. The results for both simulations are presented, compared and discussed.