A new method for establishing the total potential energy equations of steel members based on the principle of virtual work. (June 2023) - Luo, Lisheng; Zhang, Yongqiang
Abstract: The overall stability of steel members is essentially studied using the energy method. In existing literature, the expression of deformation energy is derived based on the strain energy theory of an element, which involves a complicated derivation process. Owing to the variations between the considered strain energy types and fundamental assumptions, the total potential energy equations of the steel members exhibit certain deviations. Herein, we propose a new method for establishing a total potential energy equation of steel members based on the principle of virtual work. First, an equilibrium differential equation describing the free body of steel members is derived. Subsequently, the internal forces and the restoring forces are multiplied with the corresponding virtual displacements to obtain the internal virtual work and virtual deformation energy. Finally, total potential energy equation of the steel members is obtained. In particular, the derivation process of the proposed method is simple, and each item is endowed with an explicit physical meaning. Additionally, it reveals the internal relationships between the equilibrium differential equation and the energy method, which ensures their unity. Moreover, the total potential energy equation of steel members in various common loading cases is derived based on the principle of virtual work, and the critical load is further obtained. Overall, the loading cases with exact analytical solutions are completely consistent with the exact analytical solutions. Furthermore, for cases without exact analytical solutions, theoretical derivation, finite element analyses and test results of existing literature were conducted to validate the accuracy of proposed method.