Direct method for deriving equilibrium equations in solid continuous systems

In this paper, a simplified method is proposed for deriving equilibrium equations in continuous systems. The new method is indeed the direct applying of Newton’s laws on free body diagram of point. First, by describing the concept of equilibrium equations and investigating the differences between concentrated masses and continuous systems, the physical basis of new method is introduced. It is shown that, using intensive properties simplifies the analysis of continuous systems. For verifying the new method, the governing equations in Cartesian, polar and spherical coordinates systems are derived. We have to consider nonlinear terms due to developing large slopes in system. Hence, nonlinear governing equations in Cartesian system are derived too. Finally by noting to the simplicity of new method and its independency from complicated differential and vector analysis in other methods such as Hamiltonian and classic methods, the interests of new method are emphasized. By knowing concept of physical point, a united process is accessible which is extendable to other governing equations of continuous systems.