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.

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.

Under the action of stationary random ground motion any power spectral density matrix of structural responses can be produced through the multiplication of two response vectors which are easily obtained by means of a harmonic response analysis; it is a CQC algorithm with high efficiency and simple procedure. The non-orthogonal damping matrix can be dealt with conveniently and accurately. Two examples are given to help understand the procedure of the algorithm.

An accurate and highly efficient algorithm series for structural stationary/non-stationary random response analysis, pseudo excitation method (PEM) is presented. The algorithm series, which have been developed since early 1980s, applies to the randow vibration analyses of structuses subjected to single/multiple, stationary/non-stationary random excitations, including the very attractive issuethe solution of the response to non-uniformly modulated evolutionary random excitations. Each algorithm in this series is an accurate complete quadratic combination (CQC) method because the cross-correlation quadratic terms between the participant modes and between the excitations have both been included. Such algorithms are easy to use because structural stationary random response analysis is reuced to the analysis of structural harmonic response, while structural non-stationary random responses can be readily computed in terrms of any step-by-step integration scheme (e. g. Newmark scheme or the precise integration method).