Interval mapping in structural mechanics

摘要

Structural and loading uncertainties, bounded from above and below, are considered within a finite element formulation to determine conservative bounds for the response quantities. Discretization of a continuum with material uncertainties is illustrated using a linear beam. This yields the elements of the stiffness matrix with uncertainties and the components of the force vector with uncertainties to be defined in bounded intervals. Then, the response quantities become uncertain, yet bounded in a multi-dimensional rectangular prism. The discretized linear static interval equation is solved using the triangle inequality and linear programming to determine the conservative bounds for the response quantities. For the case when only loading uncertainties are considered, the problem reduces to the pattern loading problem of structural design. The proposed formulation is applied to the structural analysis of frames with material uncertainty under static loads with uncertainties.