Influential Mode of Imperfection on Carrying Capacity of Structures

Abstract

A study of the effect of the mode of geometric imperfection on the carrying capacity of an elastic discretized structure is presented. Optimization of the mode of imperfection that causes maximum reduction in the carrying capacity of a structure is formulated. This optimization is different compared to the common practice in which a fixed mode of the paths emanating from the first critical point on the equilibrium path of a perfect structure is used as the mode of initial imperfection. The objective function to be minimized is the loading intensity at which the tangential stiffness matrix becomes singular for the first time. The constraint equations consist of equilibrium equations, singularity of the tangential stiffness matrix, and the norm of imperfections. Numerical examples are presented on elastic trusses, including a reticulated truss simulating a spherical shell, to illustrate the formulation. It was found that there was a case in which the use of a mode of paths not from the first critical point as the mode of initial guess imperfection converged to the lowest carrying capacity.