The Finite Element Method (FEM) has long been one of the most powerful computational techniques in structural engineering for the analysis of linear and nonlinear systems. Nevertheless, conventional FEM approaches may encounter significant limitations in problems involving severe geometric nonlinearity, unstable or under-constrained systems, multiple equilibrium configurations, progressive failure, and displacement constraints. To address these challenges, the Finite Element Method with Energy Minimization (FEMEM) has emerged as an alternative framework based on direct minimization of the total potential energy of structural systems.

This paper presents a comprehensive state-of-the-art review of FEMEM in structural analysis. The theoretical background of FEMEM is discussed together with its fundamental differences from classical matrix-based FEM formulations. Existing FEMEM applications on trusses, cable networks, plane-stress and plane-strain systems, and three-dimensional continuum structures are reviewed to demonstrate the capabilities of the method in solving highly nonlinear structural problems.

Particular emphasis is placed on tensegrity structures as representative examples of complex nonlinear systems. These examples demonstrate the effectiveness of FEMEM in capturing large displacements, prestressing effects, nonlinear material behavior, and multiple stable equilibrium states without requiring specialized nonlinear iterative formulations commonly employed in traditional FEM approaches.

The review also highlights the integration of FEMEM with modern metaheuristic optimization algorithms such as Harmony Search, Jaya Algorithm, Teaching–Learning-Based Optimization, and Flower Pollination Algorithm. The findings indicate that FEMEM provides a robust and flexible computational framework for advanced structural analysis and shows strong potential for future applications in adaptive, deployable, and intelligent structural systems.