Abstract
The article is devoted to the construction of model equations of the theory of elasticity with respect to deformations. Classical and new versions of boundary value problems of the theory of elasticity in strains are considered. In the classical version, model equations in strains are constructed within the framework of the Beltrami-Michell equations. A new version of model equations in strains is based on a new formulation of boundary value problems of the theory of elasticity in stresses. Discrete equations are constructed using the finite-difference method for two-dimensional problems. The well-known problem of tension a rectangular plate with a parabolic load applied on opposite sides has been solved. By comparing the numerical results of boundary value problems in classical and new formulations, as well as the Timoshenko-Goodier solution, the validity of the formulated model equations in strains and the reliability of the obtained numerical results are ensured.
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