Steel Plane Frames: Entropy and Potential Energy of Elastic Buckling Modes

The article presents a new approach for modelling initial geometric imperfections as a linear combination of scaled buckling modes obtained from elastic buckling analysis. The scale of buckling modes is calculated using Shannon entropy and potential energy. The presented case study shows that the first buckling mode is dominant, and the scale of the other buckling modes decreases. The entropy calculated from deformation presents a new perspective on buckling modes. Entropy makes distinguishing the non-sway (symmetric) and sway (antisymmetric) buckling modes possible, which is valuable if the critical loads of non-sway and sway buckling modes are close or coincide. Coupling the entropy with the potential energy of the buckling modes provides a deeper insight into the behaviour of steel frames. This proposed methodology, incorporating entropy and potential energy, offers a new and promising approach for designing structurally robust and buckling-resistant systems, empowering engineers to optimize the performance and reliability of steel frames.