Principal Virtual Work vs Principal of Minimum Potential Energy

In summary, the main difference between applying PVW and PMPE in structural problems is that PMPE calculates the actual energies involved when varying a parameter for a system, while PVW is a more difficult concept that involves satisfying two independent conditions of static equilibrium and geometrical compatibility. PMPE does not require the system to be in equilibrium or have external forces acting, while VW does. VW is useful for calculating a single displacement in a complicated set of loads.
  • #1
Abe21599
5
0
Hello

Just had a quick question for a structures class. When attempting a problem, what's the main difference between applying PVW and PMPE? What would classify a problem in using one over the other?

Thanks
 
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  • #2
OK PMPE is the calculation of the actual energies involved when we vary a parameter for a system.
The system need not be in equilibrium.
There need be no external forces acting.

For example the potential energy of a soap bubble depends on its surface area, which in turn depends on its shape, and PMPE says it will take a shape which minimises this.
Looking at shapes we find that as we vary the shape the one with the minimal surface area is a sphere, which is the shape of a soap bubble.

Virtual Work is more difficult conceptually and is not a minimum theorem. In fact the energies (work) calculated have no reality, hence the term.

The system must be in equilibrium.
There must be external forces acting.

Structural VW stems from the fact that in responding to loads any system must satisfy two independent conditions

Static equilibrium of forces (internal and external) acting (set1)
&
Geometrical compatibility of strains or displacements (set2)

Since work is the product of force and distance any such multiplication has the dimensions of work.

So multiplying set 1 by set 2 has the dimensions of work. This is known as the virtual work since either set 1 or 2 may be different from the actual ones applied to the system.

VW is particularly if we wish to calculate a single displacement of a complicated set of loads and replace the set with a single load in the direction of the desired displacement.
 
  • #3
Thanks for the detailed response. that definitely clears up a lot of things.
 

1. What is the difference between Principal Virtual Work and Principle of Minimum Potential Energy?

Principal Virtual Work and Principle of Minimum Potential Energy are two different approaches used in mechanics to solve problems involving the equilibrium of a structure or system. The main difference is that Principal Virtual Work is based on the equilibrium of virtual displacements while Principle of Minimum Potential Energy is based on the equilibrium of potential energy.

2. Which approach is more commonly used in engineering applications?

In engineering applications, both Principal Virtual Work and Principle of Minimum Potential Energy are widely used. However, the Principle of Minimum Potential Energy is more commonly used as it is easier to apply and provides more accurate results in most cases.

3. How does the Principle of Minimum Potential Energy work?

The Principle of Minimum Potential Energy states that a system will be in equilibrium when its potential energy is at a minimum. This means that the internal forces of the system will balance out with the external forces, resulting in a stable state. This principle is often used in structural design and analysis to determine the most efficient and stable configuration of a system.

4. Can both approaches be used interchangeably?

No, Principal Virtual Work and Principle of Minimum Potential Energy cannot be used interchangeably. While they both deal with the equilibrium of a system, they use different methods and assumptions to reach a solution. It is important to understand the differences between the two approaches and use them appropriately in different situations.

5. Are there any limitations to using these principles?

Like any other scientific principle, there are limitations to the use of Principal Virtual Work and Principle of Minimum Potential Energy. These principles are based on certain assumptions and ideal conditions, and in real-world scenarios, there may be factors that can affect the accuracy of the results. It is important to consider these limitations and use these principles in conjunction with other methods for a more comprehensive analysis.

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