AIRY STRESS FUNCTION Meaning and
Definition
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The "airy stress function" is a mathematical term used in the field of solid mechanics and continuum mechanics to describe a particular type of stress distribution in a two-dimensional elastic body. It is named after the British mathematician George Biddell Airy, who introduced the concept in the mid-19th century.
The airy stress function is a scalar function that satisfies the differential equations of equilibrium and compatibility for linear elasticity, which govern the stress and strain distributions in a deformable body subject to external forces. By solving these governing equations and finding an appropriate airy stress function, one can determine the stress field and displacement field in the body.
The airy stress function is employed in problems involving plane stress, where the stress is assumed to be constant along the thickness of the body. It provides a convenient way to simplify the mathematical analysis of stress distributions by reducing the problem to a single governing equation. This function is particularly useful when dealing with problems involving axially symmetric shapes, such as cylinders or spheres.
In summary, the airy stress function is a mathematical tool used to solve problems in solid and continuum mechanics, allowing for the determination of stress and displacement distributions in two-dimensional elastic bodies subject to external forces. It enables the simplification and efficient analysis of stress fields through the solution of a single governing equation.
