Effects of Rigid Body and Stretching on Nonlinear Analysis of Trusses

Abstract

According to the law of rigid body motion, a body initially acted upon by a set of forces in equilibrium will experience no additional straining when subjected to a rigid body motion, and will remain in equilibrium after the rigid body motion. When such a law is not strictly followed in an incremental‐iterative nonlinear analysis, especially in the element force recovery procedure, fictitious forces may occur at each intermediate step, which eventually may result in the deviation of the calculated behavior of a structure from its true response. From the point of view of solution accuracy, the rigid body effect plays a more important role than the stretching effect in determining which higher‐order terms should be included in a force‐recovery procedure. In this paper, both of these effects are considered in the derivation of the nonlinear stiffness matrices for a truss element. Each term involved in the formulation is examined with clear physical meanings given. Comparisons are made with previous results in the numerical examples.