Abstract
The model of an orthotropic deformable body based on the representation of stresses in terms of displacements is considered. The method of integration of three equations of the elastic equilibrium is used, based on the elimination of separate displacements. Problems related to the elimination of unnecessary functions from the representation of the general solution of the equations of the theory of elasticity are considered. Criteria are found that determine such a class of orthotropic materials that their stress-strain state can be expressed in terms of two functions. One function satisfies the equation of the second order in partial derivatives, and the other of the fourth order. It is established that the equation of the fourth order, in the general case, is not decomposed into two operator factors. Criteria were found for the expansion of a fourth-order equation into the product of two second-order equations. An equation has been written that must be satisfied by the elastic constants of an orthotropic material. The expression of deformations and stresses by introduced harmonic functions was written down.
Publisher
Ternopil Ivan Puluj National Technical University
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