DETERMINATION OF THE COEFFICIENTS OF ASYMPTOTIC CRACK—TIP STRESS EXPANSION. MIXED MODE LOADING OF THE PLATE

The aim of the study is to calculate the coefficients of M. Williams asymptotic expansion of stress anddisplacement fields using the data of finite element modeling of a plate with an inclined central crack in a uniaxial tension field. In this work, we also simulated the loading of a half-disk with a vertical and oblique notch under conditions of three-point bending. The simulation was carried out in the multifunctional software SIMULIA Abaqus. The paper proposes an algorithm for calculating the coefficients. The program, written in the MAPLE computer algebra system, allows calculating any predetermined number of M. Williams expansioncoefficients (amplitude or scale factors) and uses the values of the stress tensor components at points in the vicinity of the crack and their coordinates as input. The analysis of the influence of the number of calculated coefficients on the accuracy of their determination is carried out. Recommendations on the choice of points for calculating the coefficients are given.

Connectivity of certain simplicial complexes associated to a handlebody

In this paper, we prove three simplicial complexes associate to a handlebody, which are separating disk complex, half disk complex and disk pants graph, are connected.