Concentration of stresses in plate with two equal circular holes by tension
DOI:
https://doi.org/10.31734/agroengineering2022.26.149Keywords:
сconcentration of stresses near holes, bipolar coordinatesAbstract
In modern industry and building by project construction and machines in aircraft industry, shipbuilding, machine-building loose application find elastic details in the form of thin plates, which from different considerations loosen different kind holes. By loading such details near the holes, concentration of strains arises causing unfavourable effect on the durability of detail. Strains on the contours of holes are distributed uneven: there is small sections, which are subjected to the impact of high strains. These are the sections, where fragile cracks or plastic deformations appear, development which may result in destruction of construction.
Therefore, the study of distribution of strains near curve holes is important both from theoretical and engineering point of view.
The purpose of the present work is to provide solution of problem of the theory of elastic about concentration of stresses in plate with two equal circular holes by tension under arbitrary corner to line of hole centres.
The task of work is to define the coefficient of concentration of stresses on the contours of holes in dependence on the direction of tension and distance between the hole centres. The problem decision is in compliance with the principal function of stresses, that correspond to the strained state in unloosen hole plate. This function of stresses is added with another bi-harmonic function, which corresponds to the additional strained state, which arise because of holes.
The problem needs finding the bi-harmonic function of stresses, which satisfy the threshold conditions on the contours of holes and on infinity. Scientific novelty consists in solution of the present problem providing information about the influence on concentration made by the factor, like orientation of holes as regards to field loading in the form of tension under arbitrary corner to line of the hole centres.
Solution of the problem is presented in bipolar coordinates. The obtained formulas for stresses on contours of holes are presented. The authors have built a diagram of stresses and conducted analysis of the change of the coefficient stress concentration in dependence on the tension and distance between the hole centres.
The obtained results of the conducted theoretical coefficient of stress concentration near the holes can be used in engineering practice by construction of details in shipbuilding, airbuilding, transport and agrarian machine-building.
Result presented in the paper allow conducting theoretical substantiation of the coefficient of strain concertation near the holes and may be used in engineering practice in the time of work out details in aircraft industry, shipbuilding, machinebulding.
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