Influence of Interval Uncertainty on the Behavior of Geometrically Nonlinear Elastoplastic Structures

This paper proposes an interval analysis scheme to map out the complete bound spectrum of the most maximum and most minimum responses of geometrically nonlinear elastoplastic structures subjected to both interval applied loads and interval inelastic material properties. The proposed heuristic method uses a finite-step holonomic formulation under pseudodisplacement control. Geometric nonlinearity is modeled using a conventional second-order approximation. The analysis thus determines directly the most maximum and most minimum bound solutions by processing a pair of optimization problems, known as interval mathematical programs with equilibrium constraints or interval MPECs. The simultaneous presence of complementarity constraints and interval data is the main cause of difficulties (associated with nonconvex and/or nonsmooth optimization programs) underpinning the interval MPECs considered. The simple solution approach proposed reformulates the interval MPECs into their noninterval nonlinear programming counterparts that can be processed by a smoothing regularization technique. The efficiency and robustness of the proposed interval analysis scheme are illustrated through a number of numerical examples motivated by various engineering applications, such as the safety assessment of multistory frames that are prone to geometric nonlinearity and interval uncertainties.