Chapter 6 - Non-linear analysis of imperfect structures

Abstract

This chapter describes geometrically the non-linear analysis of imperfect structures. In specific, it describes the influence of non-linearity on the response of a structure to imperfections. The importance of non-linearity in the results depends on the specific problem considered. The chapter reviews some basic aspects of geometrically non-linear analysis, with reference to studies of imperfect shells in which this has been applied. It discusses two techniques to perform the non-linear analysis–– namely, (1) a direct method, and (2) perturbation methods. Imperfections in the geometry and in intrinsic parameters are presented using perturbation techniques. In context to the perturbation technique, the formulation differs depending on the type of imperfection. The equilibrium state using any technique of non-linear analysis should be computed first, and then perturbation has to be produced from there. Perturbations require the solution of a non-linear problem to get the reference state, and then linear problems to obtain sensitivity. In the direct method, the non-linear path has to be computed for several values of the imperfection parameter.