Abstract
The prebuckling, critical and postbuckling response of five different kinds of models is thoroughly discussed. These models are subjected to simultaneously concentrated loading and temperature variation as well as to other control parameters. More specifically: The first type of model is a rectangular two-bar frame, subjected simultaneously to axial compression and uniform temperature variation along the axes. The prebuckling, critical and post-buckling behaviour under various support conditions is investigated in detail. It is found that the temperature variation does not affect appreciably the critical state of the frame. The second type of model is a simply supported beam-column, made from an open asymmetric angle of thin-walled cross-section under axial thrust. The buckling, critical and postbuckling analysis is performed by using the variational method of Galerkin. The same model is also solved via the Finite Element Method and the results are practically coincident and satisfactory. The advantages and disadvantages of each of these methods are fully discussed. The third type of model is a one-degree-of-freedom (1-DOF) system, which consists of two rigid links of equal lengths pinned to each other. The model, which has an initial imperfection, is supported by a non-linear quadratic spring. The critical and postcritical response have been discussed also in terms of the Catastrophe Theory. The fourth type consists of four models which are one-degree-of-freedom (1-DOF) systems with various control parameters. These models are analyzed using the Catastrophe Theory after being classified into some of the seven elementary types of Catastrophes. Finally, the fifth type of model is a rectangular two-bar frame eccentrically loaded, which is studied by using Catastrophe Theory. The same frame is also analysed making use of the Finite Element Method (FEM), The results obtained from the different methods of analysis are compared and have been proved to be particularly satisfactory.