Abstract
The fundamental equations of the isotropic and orthotropic plane theory of elasticity are reworked in the frame of the generalized analytic functions theory. The areolar strain concept and its equilibrium and compatibility equations are presented. In this conception, the plane strain is decomposed into two orthogonal complex strains. A canonic form for the equilibrium equation is provided, allowing achieving its general solution in a fairly straightforward fashion. For finite rotation, new equilibrium equations and boundary conditions, in terms of strains as well as in terms of stresses, are given. Orthogonal polynomial expansions, which fulfill both the equilibrium and the compatibility equations for isotropic and orthotropic planes, are provided. These polynomials exactly retain the drilling degrees of freedom in finite element models.
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