Abstract: Abstract： The precision of finite element method is restricted by mesh density. To solve this problem, an analytical method for arbitrary complex bar system was proposed based on the nodal method. The nodal compatibility equation of displacement and the equilibrium equation of internal force were considered. The spectral coefficients were treated as the unknowns. The deformation and internal section force were described by the exact solutions of corresponding problems. The process of the construction of the coefficient matrix of the equation of the system was illustrated in an algebraic symbolic way, providing basis for general program development. Two special modelling procedures, distributed load and hinge joint, were investigated and given. A plane steel frame buckling analysis and a space pipe line harmonic analysis were launched. The results confirm that the present method is highly precise and requires a small number of elements. The method is well suited for the requirement of analytical solutions.

Key words: analytical solution, nodal method, frame, bar system, beam