Residual–Energy Flow Analysis - A Simplified Adaptive Method for Structural Systems

This paper proposes a simplified analytical framework called Residual–Energy Flow Analysis(refa) for the analysis of beams, frames, trusses, and other structural systems. The proposed method combines three fundamental concepts: equilibrium of internal and external forces,compatibility of deformation, and minimization of elastic potential energy. Unlike the classicalmoment-distribution method, which distributes unbalanced joint moments through predetermined distribution factors, and unlike the conventional stiffness method, which generally requires the assembly and solution of a global matrix, refatransfers residual force and energy information locally between connected structural elements.The central idea is to represent the structural response by a set of generalized deformationvariables and corresponding energetic participation coefficients. At each iteration, the method calculates the residual imbalance at every node, evaluates the energy required to correct that imbalance, and redistributes the correction according to the relative flexibility or stiffness of the connected members. The procedure may be implemented using scalar equations for simple structures or matrix equations for complex systems.The proposed formulation is based on the principle of virtual work, Castigliano’s theorem,the stationary potential-energy principle, and the constitutive relation between stress and strain.It can be extended to material nonlinearity, geometric nonlinearity, damage, cracking, and adaptive structural analysis. refa is presented as a theoretical research framework rather than a replacement for code-based design or validated numerical analysis. Its practical value must be established through analytical benchmarks, finite-element comparisons, and experimentalverification.