Azerbaijan National Academy of Sciences

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01.02.04

Investigation of the stabilityof the twofibersin an elasticmatrix 

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Mechanics of deformable solids

Stress state in composite materials with curved structures (piecewise homogeneous body model)

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33

3

1. Within the scope of the piecewise homogeneous body model by utilizing the geometrical linear and nonlinear exact equations of theory of elasticity and viscoelasticity it was created the bases of micro-mechanics of the composite materials with curved structures and it was solved and investigated a lot of concrete problems of this mechanics. 

2. On the base of the obtained result it was explained the "fiber separation" effect in the fracture mechanics of the composite materials.

3. The results obtained were allowed also to determine the effective mechanical constants of the composite materials with curved structures

4. It was created the continuum theory of composites with local or periodical curved structures in two directions and it was solved and investigated a lot of concrete problems of this theory

5. The aforementioned results were the base of the 4th volume (S.D. Akbarov et al. "Mechanics of materials of curved structures" NaukovaDumka, 1995, 320p. Edited by Guz A.N. and Akbarov S.D.) of the 12 volumes "Mechanics of Composites" Edited by Guz A.N.

6. At the same time, the foregoing results was considered systematically in the monograph by Akbarov S.D. and Guz A.N. "Mechanics of curved composites" Kluwer Academic Publishers, 2000, 446 p.

7. The results and investigations noted above are more actual in the present time in connection with the nanocomposites with curved structures and therefore these investigations are developed and improved with Akbarov's PhD students.

The second group investigations by Akbarov relate to the three-dimensional linearized theory of stability of the deformable solid mechanics. Note that this theory was created in the first part of the XX century by the coryphaeus of the mechanical science such as Southwell R.V. (in 1913 year), Trefftz (in 1931 -1933 years), Biezeno C.B. and Hencky H. (in 1929 year), Novojilov V.V. (in 1948 year), Neuber H. (1943 year) etc. In the second part of the XX centure this theory was developed and employed for solution of the concrete peoblems in the works by Biot M.A. (in his monogrsaph written in 1965 year), Guz A.N. ( in his monographs withhen in 1971 - 2014 years), Green A.E. and Adkins J.E. (in their monograph written in 1958 year) and etc . However, the aforementioned theory and its application were made only for the time - independent materials and element of construction made of these materials. The development of the three-dimensional linearized theory of stability of the deformable body for the time-dependent materials and its application for investigation of the concrete stability loss problems for elements of construction made of time- dependent materials was made by Akbarov.  The results by Akbarov obtained in this field can be summarized as follows.

1. It was created the three-dimensional linearized theory of stability loss of the deformable solid bodies made of time - dependent materials and this theory was applied for solution and investigation a lot of concrete stability loss problems related to elements of constructions made of time-dependent materials

2. The buckling delamination of the elastic and viscoelastic layered plates in vicinity of the inner and embedded cracks under two-axial compression along the cracks was investigated.

3. The results obtained for the stability loss problems related to the cylinders, plates and shells made of viscoelastic anisotrop with employing of the approach by Akbarov significantly differ from the results obtained by employing the well-known approximate stability loss theories. Consequently, the stability loss approach by Akbarov has not only theoretical significance, but also has a application significance.

4. The foregoing version of the three-dimensional linearized stability loss theory developed by Akbarov was also employed for the study of the internal stability loss in the structure of the unidirectional fibrous and layered viscoelastic composites.

5. The systematic consideration of the results listed above was made in the monograph by S.D. Akbarov " Stability loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites", Springer, 2012, 446 p.  

The third group investigations by Akbarov relate to the dynamics of the pre-strained bi-material elastic+elastic, viscoelastic + viscoelastic, piezoelectric + piezoelectric, elastic + compressible viscous fluid etc. systems. The results of these investigations can be summarized as follows.

1. The Lamb's problem the system consisting of the pre-stressed covering layer and pre-stressed half space were studied in the cases where the materials of the constituents are elastic, viscoelastic, piezoelectric, compressible viscous fluid etc. It  was presented the possibility to use the obtained results for improving the safety of the objects under earthquake

2. It was also studied the dynamics of the oscillating moving load action on the pre-stressed systems consisting of the elastic, viscoelastic etc covering layer and half-space. As a result of these investigations it was established the influence of the oscillation frequency on the values of the critical velocity of the moving load

3.  Torsional, axisymmetric and flexural wave dispersion in bi-material finite and small initially strained bi-material circular cylinders were studied

4. It was investigated the generalized Rayleigh wave dispersion in the system consisting of a pre-stressed covering layer and pre-stressed half-plane

Akbarov's findings above are presented in his monograph" SD Akbarov "Dynamics of pre-stressed bi-material elastic systems: a linearized three-dimensional approach," Springer, 2015, 1004 p.  

In recent years Akbarov's investigations relate to the dispersion of waves propagated in the structural elements with inhomogeneous initial stresses and to the dispersion and attenuation of these waves as a result of the viscoelasticity materials of these structural elements. The results obtained in this field have been published in many SCI-ed international journals.

2.S.D. Akbarov, A.N.Guz “Mechanics of curved composites”, Kluwer Academic Publishers, Dordrecht/ Boston/ London, 2000, 446p

3.S.D. Akbarov et al “Mechanics of composite materials with curved structures”, 1995, Naukova  Dumka, Kiev, 320p. (in Russian)

4.Akbarov S.D. On the Determination of Normalized Nonlinear Mechanical Properties of Composite Materials with Periodically Curved Layers, International Journal Solids and Structures , 1995, Vol. 32, Issue 21, Pp:3129-3143.

5.Akbarov S.D. The influence of the third order elastic constants on the dynamical interface stress field in a half-space covered with a pre-stretched layer, International Journal of Non-Linear Mechanics , 2006, Vol. 41, Issue 3, pp. 417-425.

6.Akbarov S.D. On the dynamical axisymmetric stress field in a finite pre-stretched bilayered slab resting on a rigid foundation, Journal of Sound and Vibration , 2006, Vol. 294, Issue 1, pp. 221-237.

7. Akbarov S.D. Dynamical (time-harmonic) axisymmetric interface stress field in the finite pre-strained half-space covered with the finite pre-stretched layer, International Journal of Engineering Science, 2006, Vol. 44, Issue 1, pp. 93-112.

8. Akbarov S.D. Frequency response of the axisymmetrically finite pre-stretched slab from incompressible functionally graded material on a rigid foundation, International Journal of Engineering Science, 2006, Vol. 44, Issue 8-9, pp. 484-500.

9. Akbarov S.D.Microbuckling of a doublewalled carbon nanotube embedded in an elastic matrix, Internatıonal Journal of Solids and Structures, 2013, Vol 50, Issue 16-17, Pp: 2584-2596.

10. Akbarov S.D. Buckling delamination of elastic and viscoelastic composite plates with cracks: Survey II (Axisymmetric and 3D problems), Mechanıcs of Composıte Materıals , 2013, Vol. 49, Issue 1, Pp:97-106. 

11. S.D. Akbarov “ Dynamics of pre-stressed bi-material elastic systems: linearized three-dimensional approach” Springer, 2015, 1004 p.

12. Akbarov S.D., Bagirov E. T. (2019). Axisymmetric longitudinal wave dispersion in a bi-layered circular cylinder with inhomogeneous initial stresses. JOURNAL OF SOUND AND VIBRATION, 450, pp.1-27.

13. Akbarov S.D. (co-author Negin M.) (2019). On attenuation of the seismic Rayleigh waves propagating in an elastic crustal layer over viscoelastic mantle. JOURNAL OF EARTH SYSTEM SCIENCE, 128:181

14. Akbarov S.D. (co-author Kocal T.), (2019). “The influence of the rheological parameters on the dispersion of the flexural waves in a viscoelastic bi-layered hollow cylinder”. STRUCTURAL ENGİNEERİNG AND MECHANİCS, cilt.71, ss.577-601.