FOLD LINES FOR SENSITIVITY ANALYSES IN STRUCTURAL INSTABILITY

The paper describes how a two-parameter formulation of a structural equilibrium problem can be used for a more accurate description of the occurring critical states. A fold line concept is used to evaluate the dependence of these states on an added variable, describing a disturbing load case or a disturbed geometry. The concept describes the local behaviour for small disturbances, but can also be used for parameter dependence analyses, e.g. in connection with optimization algorithms. Two different augmentations of the equilibrium relations are discussed; they describe the criticality of a solution state in different ways. Numerical adoption for a general equilibrium path following algorithm is discussed. A postponed factorization method for solution of the augmented sets of equations is proposed. Two simple examples are used to show the properties and the possibilities of the fold line concept. It is concluded that the suggested numerical procedure can give a better description of critical structural behaviour, especially with respect to imperfections in the structure and idealizations in the model.