A class of one-dimensional models for the yielding behavior of materials and structures is presented. This class of models leads to stress-strain relations which exhibit a Bauschinger effect of the Massing type, and both the steady-state and nonsteady-state cyclic behavior are completely specified if the initial monotonic loading behavior is known. The concepts of the one-dimensional class of models are extended to three-dimensions and lead to a subsequent generalization of the customary concepts of the incremental theory of plasticity.

A model for the hysteretic behavior of materials and structures is presented. This model is based on an approach which views the system as consisting of a series of ideal elastoplastic elements. The steady-state dynamic response of the model when subjected to trigonometric excitation is determined. The effect of the roundedness of the hysteresis loop on the nature of the response is investigated, and steady-state results, predicted by the theoretical model, are compared with experimental results from an actual structure.

Inelastic displacement response spectra are determined for a broad class of single‐degree‐of‐freedom hysteretic structures. Based on these spectra, effective linear period and damping parameters are defined as a function of ductility. A simple empirical formula is derived which may be used to estimate the mid‐period range inelastic response spectrum of a general hysteretic structure given the linear response spectrum of the excitation. The estimates obtained from this formula are compared with those obtained by the Newmark‐Hall method, the substitute–structure method and the ATC–3 tentative procedure. It is found that the empirical formula not only gives good estimates of the average behaviour of the inelastic spectrum, but also reproduces some of the details of the spectrum.

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A model is presented for the analysis of the response of structural systems excited by vortex shedding. The model is based on the introduction of a hidden variable to describe the fluid dynamic effects. Model parameters may be determined from experimental data for fixed and forced elements and the model used to predict the response of elastically mounted elements. Analytical model predictions are compared with experimental results for a circular cylinder.