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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. | Direct method for deriving equilibrium equations in solid continuous systems Engineering Solid Mechanics 2 2014 321-330 Contents lists available at GrowingScience Engineering Solid Mechanics homepage www.GrowingScience.com esm Direct method for deriving equilibrium equations in solid continuous systems Mohammad Asadi Dalir and Rahman Seifi Mechanical Engineering Department Bu-Ali Sina University 65175-4161 Hamedan Iran ARTICLE INFO ABSTRACT Article history In this paper a simplified method is proposed for deriving equilibrium equations in continuous Received March 6 2014 systems. The new method is indeed the direct applying of Newton s laws on free body diagram Accepted 23 August 2014 of point. First by describing the concept of equilibrium equations and investigating the Available online differences between concentrated masses and continuous systems the physical basis of new 15 October 2014 Keywords method is introduced. It is shown that using intensive properties simplifies the analysis of Equilibrium equations continuous systems. For verifying the new method the governing equations in Cartesian polar Continuous systems and spherical coordinates systems are derived. We have to consider nonlinear terms due to Direct method developing large slopes in system. Hence nonlinear governing equations in Cartesian system Intensive properties 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. 2014 Growing Science Ltd. All rights reserved. 1. Introduction The study of moving objects and their behavior analysis under external factors such as forces and moments is simply possible by using the triple laws of Newton. However all of the problems in .