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In this paper the bifurcation analysis of a circular arch under hydrostatic pressure in the elastic postbuckling range is performed by means of a geometrically exact beam model. The relevant nonlinear field equations are solved by utilizing a perturbation technique. A number of numerical results regarding the dependence of the critical load and the second order load parameter on the geometric and mechanical parameters are plotted in diagrams.

The paper presents a modification of the quasi-elastic solution technique aimed at applications to the stability analysis of viscoelastic structures. The study is concerned with two distinct instability phenomena, the bifurcation and the snapthrough buckling in the presence of creep. Respectively, two structural models are considered, a circular arch and a shallow two-bar system under sustained lateral loading. The quasi-elastic approximate solution results in the instability condition defined in terms of the load-critical time equation. The time-dependent response of the structures is studied in relation to the limited and unlimited creep behaviour of viscoelastic materials. Two numerical examples are given and accuracy of the method is discussed.

A perturbation procedure for the buckling and postbuckling analysis of elastic structures is shown to be well suited to be implemented as an automatic symbolic manipulation procedure. The postbuckling analysis of a circular arch is considered as an example, and the asymptotic description of the bifurcated equilibrium path is given. The main purposes of the automatic procedure are to generate the representation of the Frechet operator for the strain field and to perform integration by parts. This allows the manipulation of correct expressions of the basic relationships, as the strain-displacement one, without introducing any simplifying assumption or restriction. The perturbation equations are automatically generated and a solution procedure leads to parametric expressions for the coefficients of the asymptotic expansion of the bifurcated path. The symbolic manipulation system used is REDUCE.

The application of arch structural form in Iran goes back to as far as thousands of years ago. Arch is a fundamental component of Iranian architecture. Other structural systems such as vaults and domes are indeed derived from arch. In the present study, the stability of various Iranian arches with regards to weight, surcharge and earthquake has been analyzed. The most applicable Iranian arches analyzed in this study include circular arches, parabolic-shaped arches, onion-shaped arches, four-centered pointed arches, obtuse angel arches and basket-handle arches which have been transferred into ANSYS software medium following the geometrical modeling in AutoCAD software. The static analysis, modal analysis and linear and non-linear dynamic analysis have been carried out on limited components model. Having compared the results of the analyses, it was recognized that for the same span and thickness in various Iranian arches analyzed in the present study, the parabolic-shaped arch has a better bearing with respect to gravity and lateral loads, and the onion-shaped arch is void of adequate resistance under its own weight and the gravity surcharge. The static stability of the arches under the gravity load from low to high is respectively as follows: the Semi-elliptical arch, the parabolic-shaped arch, basket-handle arch, circular arch and four-centered pointed arch. Also the seismic stability of the arches is obtained from high to low as follows: the parabolic-shaped arch, the basket handle arch, the four-centered pointed arch, the Semi-elliptical arch and the circular arch. The location of cracks' threshold in the arches damaged by seismic loading is in the internal face of the arch. Also, the time and ways of arch collapse have been obtained which will be discussed in the text of the study.

The effect of creep of Perspex on its elastic modulus and on the critical load for snap–through buckling of a shallow circular arch is investigated and a comparison with elastic theory is given.