Structural instability analyses based on generalised path-following

This paper describes how quasi-static, conservative instability problems can be completely described, using generalised path-following procedures for augmented equilibrium formulations. In particular, methods for treatment of compound critical states are discussed. The numerical methods are seen as extensions to common equilibrium path methods, allowing the solution of subsets of equilibrium states, also fulfilling auxiliary relations, e.g. criticality. These formulations are in general used to describe the parameter dependence in structural response, in instability analyses and in optimisation. The paper describes the general setting of these generalised equilibrium problems, and discusses some details in their numerical treatment. Emphasis is given to the evaluation of path tangent vectors, in the presence of critical eigenvectors for the structural tangential stiffness matrix. Also, the isolation of special states, i.e. vanishing variables, turning points and exchanges of stability, is discussed. Numerical examples are used to show the possibilities and properties of the obtained solution paths, together with some aspects of the numerical procedures. (C) 1998 Elsevier Science S.A.