Determination of stress concentration near the holes under dynamic loadings

Abstract

Purpose. To develop an approach for determining the stress state of plate structural elements with holes under dynamic loads with controlled accuracy. Methodology. The study was carried out on the basis of the Laplace transform and the method of integral equations. Findings. An approach to determining the dynamic stresses at the holes in the plates is proposed, which includes: the Laplace transform in the time coordinate; a numerical method for determining transformants of displacements and stresses based on the method of integral equations; finding originals on the basis of Prudnikov’s formula adapted to dynamic problems of elasticity theory. The problem of determining the Laplace images for displacements is reduced to solving singular integral equations. Integral equations were solved numerically based on the approaches developed in the boundary element method. To find displacements and stresses, the Laplace transform inversion formulas proposed by Prudnikov are adapted to dynamic problems. The study on dynamic stresses at holes of various shapes was carried out. Originality. A new approach to the regularization of the Prudnikov formula for inverting the Laplace transform as applied to dynamic problems of the theory of elasticity has been developed. For its implementation: convergence of Fourier series based on preset stresses at the initial time is improved; the remainder is taken into account in the conversion formula. Practical value. A method has been developed for calculating the stress concentration at holes of arbitrary shape in lamellar structural elements under dynamic loads. The proposed approach makes it possible to determine stresses with controlled accuracy. The studies performed at circular and polygonal holes with rounded tops can be used in strength calculations for dynamically loaded plates. The influence of Poisson’s ratio on the concentration of dynamic stresses is analyzed.