Monogenic functions in commutative complex algebras of the second rank and the Lame equilibrium system for some class of plane orthotropy

摘要

Abstract We consider a class of plane orthotropic deformations of the form εx = σx + a12σy, γxy = 2(p − a12)Txy, εy = a12σx + σy, where σx, Txy, σy andεxγxy2,εYdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {upvarepsilon}_xrac{upgamma_{xy}}{2},{upvarepsilon}_Y $$end{document} are components of the stress tensor and the deformation tensor, respectively, real parameters p and a12 satisfy the inequalities: -1 < p < 1, -1 < a12 < p. A class of solutions of the Lamé equilibrium system for displacements is built in the form of linear combinations of components of “analytic†functions which take values in commutative and associative two-dimensional algebras with unity over the field of complex numbers.