Analysis of the stress state of a layer supported by two cylindrical swivel joints
DOI:
https://doi.org/10.46299/j.isjea.20240301.06Keywords:
layer with cylindrical cavities, generalized Fourier method, contact-type conditionsAbstract
Free body diagrams in which connections can be modeled as cylindrical swivel joints are among the most common in machine and aircraft engineering. However, there are no exact calculation methods for such schemes under given contact type conditions. Because of this, the creation of an algorithm for solving such problems is actual goal. The current investigation is devoted to the modeling of an infinite layer supported by two cylindrical swivel joints with parallel horizontal layer surfaces and each other. The swivel joints are represented as cylindrical cavities with specified contact type conditions (normal displacements and tangential stresses along the surface of the cavity are equal to zero). The stresses on the surfaces of the layer are assumed to be known. Two types of coordinate systems are used: Cartesian for the layer and cylindrical for cavities. Boundary conditions are applied to the Lamé equation. Using the generalized Fourier method, the problem is reduced to solving a system of infinite linear algebraic equations, which is solved by the reduction method. The numerical study was carried out with the accuracy of fulfilling the boundary conditions 10-3 for stress values from 0 to 1 at the fourth order of the system of equations. The analysis of the stress state was carried out for the supporting parts of the layer and the upper boundary of the layer. A comparison was made with the results of the study for a similar task with fixed supports. It was noted that the circumferential stresses in the layer along the surface in contact with the swivel joint, when the contact type is fastened, compared to the rigid fastening, has the opposite sign, which can be essential for materials with different tensile-compressive characteristics. The current method can be used to analyze the stress-strain state of a bolted or riveted connection in which the tightening moment changed during operation and the connection turned from rigid to hinged.References
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