The force density method (FDM) is a classical method for form finding and static analysis of membrane-cable-strut-beam hybrid structures (HS). This study focuses on the energy principle of FDM, and establishes the potential energies for HS in the form-finding and static analysis stages. The HS model is discretized into link, T and beam elements. Equilibrium equations and stiffness matrices are formulated using the principle of stationary potential energy. In the integrated analysis, the compatibility between the link and beam element is resolved by adopting (x, y, z, θx, θy, θz) as degrees of freedom (DOF) and transforming the beam's DOF into coordinate differences. The global matrix is assembled using nodal global DOF numbers, showing a computational advantage over the conventional topological matrix method. FDM has demonstrated consistency in form-finding and static analysis stages by applying constant and elastic force densities. The algorithm has been implemented in a program called TMCAD with all the calculation details illustrated, and FDM's effectiveness is verified through five HS examples.