MATHEMATICAL MODELING OF THE STRAINED STATE IN BROAD PIVOTS WITH TWO CIRCULAR HOLES BY CROOK
DOI:
https://doi.org/10.32718/agroengineering2025.29.145-150Keywords:
concentration of stresses near holes, biharmonic functions of stresses, bipolar coordinatesAbstract
It has been observed that elastic components, such as thin plates, are widely used in the design of structures and machines across aviation, shipbuilding, and mechanical engineering. However, these parts are often weakened by various holes for several reasons. When such components are subjected to loading, stress concentrations tend to occur near the holes, which can negatively impact their strength. The distribution of stresses around the edges of the holes is uneven, leading to small areas that experience significantly high stresses. It is in these places that brittle cracks or plastic deformations can develop, potentially resulting in structural failure.
Studying the distribution of stresses near curved holes is crucial from both theoretical and engineering perspectives.
This work presents a solution to the problem of stress concentration in broad pivots featuring two unequal circular holes by crook. The solution is based on a fundamental stress function associated with the stress state in a rod that does not have any holes, to which a second biharmonic function is added. This additional function represents the stress state that arises due to the presence of the holes. The challenge lies in determining the biharmonic stress function that satisfies the boundary conditions at the contours of the holes and extends out to infinity. The scientific novelty of this work is that it provides insights into how the orientation of holes relative to the field of crook loads influences stress concentration. The solution is presented in bipolar coordinates, and formulas for the stresses along the contours of the holes are derived. Additionally, the known result for the displacement of a crook pivots with a single circular hole is included. The obtained stress values along the contours of the holes for certain special cases are also reported.
The findings of this study enable the theoretical determination of the stress concentration factor near the holes and can be effectively applied in engineering practice when designing components in shipbuilding, aircraft construction, and mechanical engineering.
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