# On the analysis of neutral holes

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## Abstract

When an opening must be located in a tension panel the inevitable stress concentration that results can be reduced if the edge of the opening is reinforced. While there is a variety of solutions for providing reinforcements which reduce stress concentrations in the panel, none of these consider the state of stress that exists in the reinforcement.

This paper extends the theory of neutral holes to consider bending of the reinforcement as well as to allow for the use of a different material in the reinforcement. Photoelastic experiments demonstrate the effectiveness of neutral holes for uniform uniaxial tension panels for which the opening consists of parabolic sections.

## Keywords

Mechanical Engineer Fluid Dynamics Stress Concentration Uniaxial Tension Reduce Stress Concentration## List of Symbols

- ϕ
Airy stress function

- \(\left. \begin{gathered} \sigma _x = \frac{{\partial ^2 \phi }}{{\partial y^2 }} \hfill \\ \sigma _y = \frac{{\partial ^2 \phi }}{{\partial x^2 }} \hfill \\ \sigma _{xy} = - \frac{{\partial ^2 \phi }}{{\partial x\partial y}} \hfill \\ \end{gathered} \right\}\)
plane stress components

- ψ
inclination of boundary to

*x*-axis*P*axial force in reinforcement boundary

*t*panel thickness

- σ
_{0} uniaxial-tensile stress in

*y*-direction*P*_{V},*P*_{H}vertical and horizontal components of force in reinforcement

*A*_{r}area of reinforcement cross section

*E*_{r}reinforcement modulus

*E*_{p}panel modulus

*ν*_{p}Poisson's ratio for panel

*ε*_{ψ}strain parallel to boundary of reinforcement

*r*arbitrary parameter for size of reinforcement

*A*_{t}area of cross section of vertical reinforcement

*σ*_{t}stress in vertical reinforcement member

*A*_{c}area of cross section of compressive reinforcing member

*σ*_{c}stress in compressive reinforcing member

*M*bending moment in reinforcement

*σ*_{r}mean tensile stress in reinforcement

*f*stress-optical coefficient

*n*fringe order

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## References

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