Stress-deformed state in the plane domain boundary angle cutout zone

Abstract

Studying the stress-deformed state of structures with complex-shaped boundary is an urgent task for designing and developing numerical and analytical methods of constructions, buildings and structures research. Stress concentration due to geometrically nonlinear shape of the boundaries – cutouts, notches, causes stress, deformation zones with significant magnitudes and gradients. Theoretical analysis of the boundary angle cutout domain stress-deformed state (SDS) under rupturing forced deformations comes down to studying singular solutions of elasticity theory homogeneous problem with power-type specifics. Novelty of the studies given herein is that the SDS in the vicinity of an irregular boundary point – the domain boundary angle cutout vertex, is characterized by stress limit values similar to stress intensity coefficients when applying force criteria in fracture mechanics. Asymptotics of elastic problem solution in the random opening boundary angle cutout domain is written using the stress limit values. Obtained asymptotic expression for elasticity theory plane problem solution allows to analyze the SDS of the domain boundary angle cutout zone as a function of the domain cutout opening angle, mechanical characteristics and eigenvalues of elasticity boundary-value problem in case of stresses homogeneous boundary conditions.