Abstract
A methodology of structural integrity analysis via convex model of uncertainty is presented for structures that are subject to the uncertain ground motion caused by earthquakes. The ground motion is represented in terms of a truncated Fourier series, and the Fourier coefficients are assumed to fluctuate uncertainly. The uncertain fluctuation of the coefficients is bounded within convex hulls so as to introduce a convex set representing the characteristic information of the earthquake, that is, the power spectrum. An undesirability index is adequately defined in order to indicate the degree of undesirability of structural integrity. The fluctuation of the undesirability index is submitted to first-order approximation with respect to the uncertain Fourier coefficients through finite element sensitivity analysis. The worst case, which produces the maximum value of the undesirability index during the observation period, is identified using the Lagrange multiplier method with equality constraints for the uncertain Fourier coefficients by the boundary of the convex hulls. The validity of the proposed formulation is proven through numerical examples using a planar portal frame that is subject to artificial and observed earthquake ground motions.
