Elastic nonlinear behavior of truss system under follower and non-follower forces

Abstract

This paper presents a nonlinear analysis of elastic plane and space trusses, incorporating buckling of individual member(s) of the trusses. The nonlinear equilibrium equations are expressed as relations between force intensity and positions of free nodes. Using this approach, the nonlinear behavior under both follower and non-follower forces can be formulated in a concise and simple way. When a member buckles, an additional degree of freedom, the (equal) buckling angles of end nodes appear. At this state, a member has two governing differential equations. From the first governing differential equation and using elastica solution, its corresponding nonlinear equilibrium equation is derived. On the other hand, the second governing differential equation leads to a nonlinear relation between buckling angle and positions of end nodes which serves as an additional equation to accommodate the above additional degree of freedom. The versatility of the proposed analysis is first applied to simple two bar plane truss, under both follower and non-follower forces and then to more complex plane and space trusses.