Abstract
The authors discuss the linear elasticity model with a structural parameter. The system of the constitutive relations is composed of five independent equations. The classical elasticity theory only contains three equations. The additional two equations are contained in the hypothesis of diffeomorphism—the assumed smoothness of the field of displacements, and are not explicitly formulated in the classical theory. The withdrawal of the smoothness of the displacement field gives rise to a correction for local bends, and the two additional equations are to be formulated explicitly. These considerations result in the linear elasticity model with a structural parameter. In the static variant of the model, macrostrains depend on stresses and on the second differential coefficients of stresses with respect to coordinates. The authors use the model to analyze the problem on tension of a rectangular plate with a circular hole (Kirsch problem). The numerical solution is obtained, and the isolines of the calculated stresses are plotted. The influence of the structural parameter on the stress concentration in the plate is evaluated.
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