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DEVELOPMENT OF THE “SEPARATED ANISOTROPY” CONCEPT IN THE THEORY OF GRADIENT ANISOTROPIC ELASTICITYстатья
- Авторы: BELOV P.A., LURIE S.A.
- Журнал: Mechanics of Composite Materials
- Том: 57
- Год издания: 2021
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- DOI: 10.1007/s11029-021-09966-x
- Аннотация: A variation model of the gradient anisotropic elasticity theory is constructed. Its distinctive feature is the factthat the density of potential energy, along with symmetric fourth- and sixth-rank stiffness tensors, also containsa nonsymmetric fifth-rank stiffness tensor. Accordingly, the stresses in it also depend on the curvatures and thecouple stresses depend on distortions. The Euler equations are three fourth-order equilibrium equations. Thespectrum of boundary-value problems is determined by six pairs of alternative boundary conditions at eachnonsingular surface point. At each special point of the surface (belonging to surface edges), in the generalcase, additional conditions arise for continuity of the displacement vector and the meniscus force vector whencrossing the surface through the edge. In order to reduce the number of the physical parameters requiringexperimental determination, particular types of the fifth- and sixth-rank stiffness tensors are postulated. Alongwith the classical tensor of anisotropic moduli, it is proposed to introduce a first-rank stiffness tensor (a vectorwith a length dimension), with the help of which the fifth-rank tensor is constructed from the classical fourthranktensor by means of tensor multiplication. The sixth-rank tensor is constructed as the tensor product of theclassical fourth-rank tensor and two first-rank tensors.
- Добавил в систему: Белов Петр Анатольевич