Analysis of under-constrained and unstable structures by the method TPO/MA

Under-constrained and unstable structures are those which are kinematically unstable. They may show large displacements even under very small forces contrarily to well-constrained stable structures. Under-constrained structures manifest themselves with insufficient boundary conditions. On the other hand, structures with missing members may become kinematically unstable under certain loadings. A common property of these structures is that the rank of their stiffness matrix, used in their analysis by classical methods, comes out to be zero, thus making impossible their analysis by these methods. Fortunately, application of the method Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) makes the analysis of these structures very simple, with no extra difficulty as compared to the analysis of well-constrained stable structures. Examples shown in this study are demonstrating this fact.