The principle of virtual work is a powerful tool used in the field of mechanics to analyze the equilibrium and stability of elastic systems. It states that for a system in equilibrium, the total virtual work done by both internal and external forces is zero.

The virtual work refers to the work done by hypothetical or virtual displacements, which are small and arbitrary displacements applied to the system. These displacements are used to analyze the system's response to external forces and determine the equilibrium conditions.

To apply the principle of virtual work to an elastic system, we need to consider both the internal and external forces acting on the system. Let's discuss each of these forces in detail:

a) Internal forces only:
Considering internal forces alone would not give us a complete understanding of the system's behavior. Internal forces include the forces generated within the system due to deformations and stresses. These forces are responsible for maintaining the equilibrium of the system. However, by considering internal forces alone, we would neglect the influence of external forces that act on the system.

b) External forces only:
Similarly, considering only external forces would also not provide a comprehensive analysis of the system. External forces are applied to the system from the outside and can include loads, applied forces, and boundary conditions. While external forces determine the overall behavior of the system, neglecting internal forces would lead to an incomplete understanding of the system's equilibrium.

c) Internal as well as external forces:
To fully analyze the equilibrium and stability of an elastic system, we must consider both internal and external forces. By considering both types of forces, we can account for the internal stresses and deformations within the system as well as the external forces acting on it. This comprehensive analysis allows us to determine the conditions under which the system remains in equilibrium.

By considering both internal and external forces in the principle of virtual work, we can accurately predict the equilibrium conditions of an elastic system. This principle is widely used in various fields of engineering, such as structural analysis, solid mechanics, and finite element analysis, to design and analyze complex systems.

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