Finite Element Method (FEM) is a powerful and widely used numerical technique for the analysis of structures and systems in structural engineering. While FEM is highly effective for linear problems and can address certain classes of nonlinear problems through appropriate iterative schemes, there are structural analysis situations that cannot be satisfactorily solved using traditional or improved FEM formulations. These situations include non-unique equilibrium states, nonlinear or incomplete boundary conditions, and structures with ill conditioned elasticity matrices, lattice systems following the failure of one or more elements, tensegric structures, etc. Further examples can be given from progressive analysis of structures where FEM becomes inapplicable after some point. To overcome these limitations, an emerging approach, Finite Element Method with Energy Minimization (FEMEM), has been introduced. FEMEM is based on the same starting point with FEM; however, it is based on potential energy of elements instead of static equilibrium of elements. Instead of solving matrix equations, FEMEM formulates the problem as the minimization of a functional, namely the total potential energy of the structure.

This presentation introduces the fundamental concepts of FEMEM, with stress on optimization concepts, then provides a comparative discussion with classical FEM to highlight the advantages and limitations of the method. Finally, directions for future research will be  discussed, with an emphasis on extending the applicability of FEMEM to more complex structural systems and a wider range of nonlinear effects, including material, geometric, and constraint-related effects.