Effect of the boundary conditions on the stress concentration in thin functionally graded plates with a circular opening

Plate-shell structural elements with openings are widely used in various branches of engineering, including the space-rocket, the oil-and-gas, and the power industry, construction, etc. The presence of openings leads to a sharp increase in local stresses, which, under certain conditions, may cause a failure. The use of inclusions, in particular made of functionally graded materials (FGMs) with certain mechanical properties, allows one to significantly reduce the stress concentration in the vicinity of local concentrators, thus increasing the strength and reliability of the structure as a whole. This work presents the results of numerical simulation and finite-element analysis of the stress and strain field of thin plates in the presence of a circular opening and a surrounding annular inclusion under various boundary conditions. The effect of the geometric and mechanical parameters of FGM inclusions on the stress and strain concentration in the vicinity of the opening is investigated. The distribution of the stress and strain intensities in the zones of local stress concentration is obtained. For each of the boundary conditions considered, advisable parameters of annular FGM inclusions are found such that the stress concentration factor is reduced by ~ 40 - 56 per cent. At the same time, a proportional decrease in the stress intensity in the vicinity of the opening is also observed. The law of variation of the elastic modulus of the FGM inclusion and the width of the inclusion have a significant effect not only on the magnitude of the stress and strain concentration, but also on the stress pattern. The results of large-scale computational experiments show that the use of an annular FGM inclusion with FGMs makes it possible to reduce both the stress and the strain intensity in the vicinity of the opening. Thus, the use of annular reinforcements around circular openings in plates under various boundary conditions is reasonable because such reinforcements allow one to reduce the stress concentration by smoothening the stress distribution.