On unbalanced forces in 3D elasto-plastic FEM analysis

This paper focuses on properties of unbalanced forces in 3D elasto-plastic calculation. The relationship among unbalanced forces, reinforced force and structural stability is established. It is revealed that a structure is stable if a reinforced force with the same magitude as the unbalanced force but in the opposite direction is added. Furthermore, the elasto-plastic theory always minimizes the actual unbalanced force or reinforced force in the sense of a condition number in the norm of complementary energy.A case study for an arch dam shows that the analysis of unbalanced force is helpful to evaluate the structural stability and reinforcement.