New analytical approach for geometrically nonlinear buckling analysis of a inclined rod using the arc length method

Abstract

This paper is concerned with nonlinear buckling problem of inclined rod subjected to concentrated loads and moments at the ends. Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions. This work introduces a new analytical approach to construct the governing equations considering large displacement. The mathematical formulation based on geometrical compatibility, equilibrium of forces and moments and constitutive relations considering large displacements. The geometrical compatibility relationship is getting from integrating along the elastic curve of the deformed rod. A system of nonlinear and integral equations with boundary conditions prescribed at both end is constructed. Using the arc length technique the paper developed incremental-iterative algorithm for solving the system of nonlinear equation. Based on the proposed algorithm, the paper established the calculation procedure and the programs for determining the equilibrium path for generally supported inclined rod subjected to concentrated loads and moments at the end.