Airy Stress Func. Polynomial order to satisfy the biharmonic equation

Thread starter StevenScott
Start date Dec 29, 2017
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Polynomial Stress Stress analysis

In summary, the Airy Stress Function is a mathematical function used in elasticity to describe the stress distribution in a solid body. It is used to solve engineering problems by providing a mathematical representation of the stress distribution. The appropriate polynomial order must be chosen to ensure accuracy and efficiency, which is determined based on the complexity and geometry of the problem. However, the Airy Stress Function has limitations such as only being applicable to linear elastic materials and two-dimensional problems, and not accounting for material nonlinearity or plasticity.

Dec 29, 2017

StevenScott

Hello,

When choosing a polynomial stress function Φ to satisfy the biharmonic equation, how does once decide on which order of the polynomial to choose?
For example, is it based upon the number of boundary conditions, like a 3rd order polynomial would satisfy 3 boundary conditions?

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Dec 31, 2017

Mike Stefan

You are right.

1. What is the Airy Stress Function?

The Airy Stress Function is a mathematical function used in the theory of elasticity to describe the stress distribution in a solid body subject to external forces. It is a scalar function that satisfies the biharmonic equation in two-dimensional Cartesian coordinates.

2. How is the Airy Stress Function used to solve engineering problems?

The Airy Stress Function is used to solve engineering problems by providing a mathematical representation of the stress distribution in a solid body. This allows engineers to analyze the behavior and stability of structures under various loads and boundary conditions.

3. What is the importance of choosing the appropriate polynomial order for the Airy Stress Function?

The polynomial order of the Airy Stress Function directly affects its accuracy in representing the stress distribution in a solid body. Choosing too low of an order can result in inaccurate solutions, while choosing too high of an order can lead to computational inefficiencies.

4. How is the polynomial order determined for a specific engineering problem?

The polynomial order is typically determined based on the complexity and geometry of the engineering problem. It may also be influenced by the desired level of accuracy and computational resources available. Higher order polynomials are generally used for more complex problems or when a high level of accuracy is required.

5. Are there any limitations to using the Airy Stress Function?

While the Airy Stress Function is a powerful tool for solving engineering problems, it does have some limitations. It is only applicable to linear elastic materials and two-dimensional problems. Additionally, it assumes small deformations and does not account for material nonlinearity or plasticity.