Open AccessMathematical Modeling of Boundary Stress State of Orthotropic Material
Author(s) -
Sofia Holovata,
Yaroslav Sokolovskyy,
Bohdan Pobereyko,
Andriy Holovatyy
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1016/1/012001
Subject(s) - orthotropic material , deformation (meteorology) , boundary value problem , stress (linguistics) , nonlinear system , boundary (topology) , anisotropy , mathematical analysis , stress functions , mathematics , materials science , mechanics , structural engineering , physics , finite element method , composite material , engineering , optics , linguistics , philosophy , quantum mechanics
In the paper, the mathematical model for determination of stress and deformation fields inside and at the elastic region boundary of deformation of orthotropic materials under the biaxial loadings is developed. Within the proposed model, a mathematical model for determination of the material transition boundary from elastic into non-elastic deformation region is developed and a system of nonlinear equations for calculation of the values of its parameters is obtained. By using the continuous method of solution continuation with respect to the best parameter and Runge-Kutta method, the demarcation curves of absolutely elastic and non-elastic deformation regions for the pine tree are constructed. The analysis of the obtained curves is carried out and on its base it is shown that the proposed model, in contrast to the known mechanical theories of strength, makes possible to determine and substantiate the ultimate stress states of materials whose asymmetry coefficients of the boundaries of proportionality in some anisotropy directions are greater, and in others less than one.