Calculation of Rod Elements with Cracks Based on a Combination of Rod Theory and Elasticity Theory

Abstract

Mathematical models are presented for calculating the stress-strain state of rods with cracks under tension-compression and bending deformations. The work uses a combination of the relations of elasticity theory and rod theory. The main provisions of the proposed modeling method are based on dividing the rod into fragments and finding, for each of the selected fragments, deformations and stresses based on rod theory or elasticity theory. Calculation algorithms are described, which are relatively simple to implement. In order to confirm the reliability and accuracy of calculations based on the proposed models, results from solving problems are presented.