The discrete element method has been applied successfully to the elastic analysis of a wide variety of highly non-linear problems in structures under conditions of gross deformations. For certain types of frame it has been found possible to program this method of second-order analysis and account satisfactorily for large deformations so that one can produce solutions satisfying equilibrium and compatibility almost anywhere in the load-deformation field. The method was first applied by the author to suspension cables and inflatable dams which are structures for which a linearelastic analysis is inappropriate if not meaningless. It was later extended to deal with flexurally stiff elements and it subsequently provided some interesting insights into the nature of equilibrium bifurcation states for symmetrically loaded arches, rings and portal frames. The problem with the method is that it is difficult to generalise it so that the one program will handle a wide range of structural forms as is the case with frame stiffness programs and finite element packages. Thus far, the discrete element method has been successful in applications to frames forming a single closed loop such as beams and beam-columns, rings, arches and portal frames. The paper concludes with a description of attempts to extend the method to multi-storey and multi-bay frameworks.
The forms of structure devised by designers have often been determined by the available analytical methods. But the various methods of structural analysis have been difficult to classify. One can think of the material behaviour and refer to plastic as compared with elastic methods. Alternatively one may consider the nature of the deformations occurring in the structure under real or ultimate loading conditions. The deformations may be small, finite or large. Some structures may be very stiff and deform very little under normal conditions.