Virtual work

Definition

Virtual work refers to the work done by forces during a virtual displacement, which is an imagined or hypothetical displacement that is consistent with the constraints of a system. This concept is important in mechanics, particularly in the analysis of systems in equilibrium, where it allows for the evaluation of forces and displacements without the need for dynamic analysis. Understanding virtual work provides a powerful method for deriving equations of motion and analyzing mechanical systems.

5 Must Know Facts For Your Next Test

1. Virtual work can be applied to both conservative and non-conservative forces, making it a versatile tool in mechanics.
2. In a system at equilibrium, the total virtual work done by external forces is equal to the total virtual work done by internal forces.
3. The concept of virtual work is used to derive equations of motion in both rigid body dynamics and continuum mechanics.
4. When analyzing a mechanical system, identifying constraints is crucial as they dictate the allowable virtual displacements.
5. The virtual work principle can be used to solve complex problems more easily than traditional methods like Newton's laws.

Review Questions

• How does the concept of virtual work facilitate the analysis of mechanical systems at equilibrium?
  • Virtual work allows for evaluating mechanical systems by considering hypothetical displacements consistent with constraints without requiring dynamic analysis. In equilibrium, the total virtual work done by external forces matches the internal forces, ensuring that all conditions of balance are met. This approach simplifies the problem-solving process by enabling engineers to focus on forces and displacements rather than calculating motion directly.
• Discuss how D'Alembert's principle relates to the concept of virtual work and its application in dynamics.
  • D'Alembert's principle integrates concepts from both dynamics and statics by stating that the sum of external forces and inertial forces equals zero. This relationship allows for utilizing virtual work to analyze systems in motion as if they were in static equilibrium. By applying virtual work within this framework, engineers can derive equations that account for both forces and inertial effects, facilitating a deeper understanding of dynamic behavior.
• Evaluate how understanding virtual work influences problem-solving strategies in engineering mechanics.
  • Grasping virtual work significantly enhances problem-solving strategies by enabling engineers to analyze complex mechanical systems using simplified principles. It allows for a focus on energy methods and balances without detailed kinematic analyses, which can be cumbersome. By employing virtual displacements, engineers can quickly assess stability and force distribution while maintaining compliance with constraints, ultimately leading to more efficient design processes.

Related terms

D'Alembert's principle: A principle stating that the sum of the differences between the forces acting on a system and the inertial forces is zero, allowing for static equilibrium analysis in dynamics.

Work-energy principle: A principle that states the work done by all forces acting on an object is equal to the change in its kinetic energy.

Constraints:

Conditions that limit the motion of a system, which must be considered when analyzing virtual work and displacements.