A new methodology to obtain the exact solutions of isotropic plane beam subjected to arbitrary loads

A general method is established to obtain the exact solutions for isotropic plane beam subjected to arbitrary loads with various ends conditions. Contrasting with the traditional trial-and-error method, the most advantage is it does not need to guess and modify the stress function repeatedly and obtain the exact solutions directly. Firstly, the general solution of the plane beam governing equation is given, which contains four unknown functions. Secondly, the four functions are derived by simplifying the four functional equations. Finally, the remaining unknown constants are determined by virtual of the boundary conditions of two ends of the beam. Several examples show the correctness of this general method.