Discrete-Element Methods for Stability Analysis of Complex Structures

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Abstract
The matrix methods of structural analysis developed specifically for use on modern digital computers have now become universally accepted in structural design. These methods provide a means for rapid and accurate stress and deflection analysis of complex structures under static and dynamic loading conditions and they can also be used very effectively for the stability analysis. In the conventional stability analysis two possible approaches are normally used; either the differential equations describing the structural deflections are formulated and the lowest eigenvalue representing the buckling load condition is found for a given set of boundary conditions, or alternatively, if the differential equations are too difficult to prescribe, approximate deflection shapes are used in the strain energy expression for large deflections which is subsequently minimised, leading to the stability determinant whose lowest root represents the instability condition. When designing complex structures the conventional methods of finding buckling load conditions are extremely difficult to apply, and therefore in such cases we have to rely on the matrix methods of stability analysis.