GENERAL SCALARIZATION METHOD OF DYNAMIC ELASTIC FIELDS IN TRANSVERSALLY ISOTROPIC MEDIA AND ITS NEW APPLICATIONS

Introduction. An efficient technique of tensor field scalarization  is  successfully  used  while  investigating  tensor  elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be exp...

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Bibliographic Details
Main Authors: I. P. Miroshnichenko, V. P. Sizov
Format: Article
Language:Russian
Published: Don State Technical University 2018-09-01
Series:Advanced Engineering Research
Subjects:
Online Access:https://www.vestnik-donstu.ru/jour/article/view/1341
Description
Summary:Introduction. An efficient technique of tensor field scalarization  is  successfully  used  while  investigating  tensor  elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be expressed through the scalar potentials corresponding to the quasi-longitudinal, quasi-transverse, and transverse-only waves. Such scalarization is possible if the objects under consideration are tensors relating to  the subgroup  of general coordinate conversions, when the local affine basis has one invariant vector that coincides with the material symmetry axis of the material. At this, the known papers consider structures where this vector coincides with the normal to the boundary between layers. However, other cases of the mutual arrangement of the material symmetry axis of the  material  and  the boundaries between layers are of interest on the practical side.Materials and Methods. The work objective is further development of the scalarization method application in the boundary value problems of the dynamic  elasticity theory for the cases of an arbitrary arrangement of the material symmetry axis relative to the boundary between layers. The present research and methodological apparatus are developed through the general technique of scalarization of the dynamic elastic fields of displacements, stresses and strains in the transversally isotropic media.Research Results. New design ratios for the determination of the displacement fields, stresses and deformations in the transversally isotropic media are obtained for the cases of an arbitrary arrangement of the material symmetry axes of the layer materials with respect to the boundaries between layers. Discussion and Conclusions. The present research and methodological apparatus are successfully used in determining the stress-strain  state  in  the  layered  structures  of  transversally isotropic materials, and in analyzing the diagnosis results of the state of the plane-layered and layered cylindrical structures under operation.
ISSN:2687-1653