Nonlinear Finite Element Analysis of Frames Under Interval Material and Load Uncertainty

Abstract

The present study focuses on the development of nonlinear interval finite elements (NIFEM) for beam and frame problems. Three constitutive models have been used in the present study, viz., bilinear, Ramberg–Osgood, and cubic models, to illustrate the development of NIFEM. An interval finite element method (IFEM) has been developed to handle load, material, and geometric uncertainties that are introduced in a form of interval numbers defined by their lower and upper bounds. However, the scope of the previous methods was limited to linear problems. The present work introduces an IFEM formulation for problems involving material nonlinearity under interval material parameters and loads. The algorithm is based on the previously developed high-accuracy interval solutions. An iterative method that generates successive approximations to the secant stiffness is introduced. Examples are presented to illustrate the behavior of the formulation. It is shown that bounding the response of nonlinear structures for a large number of load combinations under uncertain yield stress can be computed at a reasonable computational cost.