• Solid Mechanics

• Calculation on stress concentration around a hole under planar stress status

A linear elastic analysis is given for a square board with a center hole as shown below, which undertakes the pulling loading from both the upper and the lower sides. The side length is 100 mm, the radius of the hole is 10 mm and the loading of 100 N/m is uniformly distributed. The material properties are as follows: Its Young's modulus is  2.0e5N/mm² and its Poisson ratio is 0.3. The stress distribution within the board, especially the stress concentration phenomenon around the hole is investigated.

The controlling equations of solid deformation include:

• the force balance equations 

• the force balance equations 

• the constitutive relation between the strain and the stress

          ,

where and are the elastic modulus and the Poisson ratio of the material, separately.               

Comparison between the solutions by use of FEM and analytical method:

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