Applications of common energy variability methods for establishing the equilibrium equation in mechanics

Abstract

The principles of the energy variation method are commonly utilized in mechanics. Energy is a scalar variable, so these are more convenient and simple to establish the equilibrium equations compared to vector-based approaches (i.e. using forces and displacements). The present article applied the theorem of the energy variation method in order to set the equilibrium equations for various complicated problems. Four examples of applying the energy variation method include the differential equation of the Euler – Bernoulli beam based on the energy method, the system of Equilibrium Equations of the Euler–Bernoulli beam with the theorem of Least Work, the principle of maximum work to establish the equation of motions for the Euler–Bernoulli beam and the equation of motion for the Euler–Bernoulli beam by the virtual work theorem, have been implemented. The results obtained from this study open up further research directions on the application of the energy variation method in mechanics as well as in the analysis theory of beam bridges.