A simple and accurate algorithm for nonstationary responses of structures subjected to evolutionary random seismic excitation is presented as an extension of the pseudo-excitation method for stationary random seismic responses. The analyses of various time-dependent auto- or cross-power spectral density (PSD) functions have simple and unified formulae. For some important envelope functions, time-dependent PSD functions can be calculated by means of simple frequency-domain analyses.

In this paper, a bi-factor a-β algorithm based on the Kuhn-Tucker criteria about the minimal weight design of a structure under statical and dynamical constraints, is presented. Among the constraints, that of “frequency-prohibited band” is a new formulation which requires any characteristic frequency of the structure not to fall into a certain frequency region. The desing variables may cover sizes of the elements and/or coordinates of the nodes. The upper and lower bounds of each variable are specified, and the stress constraints based on full-stress criteria may also be taken into account. Satisfactory results have been obtained over varous examples wherein the stiffness and/or mass matrices of the structure may be highly nonlinear about the design variables.