INTERVAL ALGEBRA TO DEAL WITH PATTERN LOADING AND STRUCTURAL UNCERTAINTIES

Structural and loading uncertainties, bounded from above and below, ar e considered within a finite-element formulation to determine conserva tive bounds for the displacement and force response quantities. Discre tization of a continuum with material uncertainties is illustrated usi ng a linear elastic beam. This yields the elements of the stiffness ma trix with uncertainties and the components of the force vector with un certainties, to be defined in bounded intervals. Then, the response qu antities become uncertain, yet bounded, in-a multidimensional rectangu lar prism. The discretized linear static interval equation is solved u sing the triangle inequality and linear programming to determine the c onservative bounds for the response quantities. For the case when only loading uncertainties are considered, the problem reduces to the patt ern loading problem of structural design. The proposed formulation is applied to the structural analysis of frames with material uncertainty under static loads with uncertainties.