**KULIYEV SABIR ALI OGLU**

Dr. of Techn. Sci. prof. of the chair
“Theoretical mechanics”
Azerbaijan Architectural
Civil Engineering University

1. First in the scientific world, the functions mapping the complex contours with different linear cracks on the exterior of a unit circle (**circle, ellipse, square,** **hexagon and etc. with various linear cracks**). The specialist know well the role of these **conformally mapping** functions for the problems of elasticity theory.

2. Choice of analytic functions used by solving boundary value problems of elasticity problem was generalized and useful recommendations for a complicated geometry domains are given. If the given problem is reduced to finding a function regular everywhere on the exterior of internal contour, then this function is taken in the form of a series with negative degree of variable, and vice versa, if this problem is reduced to finding a function everywhere regular interior to the contour of domain, it is taken in the form of **Fourier series**.

3. The auxiliary function method of the famous scientist **prof. D.I. Sherman** was generalized and developed. **Prof. D.I. Sherman** introduced auxiliary functions mainly on circles, but **prof. S.A. Kuliyev** introduces these functions on arbitrary contours including on the contours with different linear cracks. Therewith the solution of the considered problem of theory of elasticity is reduced to finding one analytic function.

4. Problems of flexion of a polygonal multi-connected plate with different linear crack were solved both in **isotropic and in anisotropic statement**.

5. First in the scientific world, the problems of flexion and torsion of prismatic beams made of **isotropic or anisotropic materials** were solved.

6. Plane problems of theory of elasticity with regard to **physical nonlinearity** of the material were solved.

7. Problems of **flexion and torsion of prismatic beams** were solved in **physically nonlinear statement**.

8. Problems on definition of stress strain state of a polygonal plate weakened by archwise cracks were solved.

9. Problems on definition of stress strain state of a polygonal multi-connected plate with different cracks under **uniform torsion** were considered, critical values of angular velocity for concrete cases were found.

10. Problems on free **flexural oscillation** of a polygonal plate with different linear cracks were solved, frequency of oscillations depending on sizes of a plate and also on fastening of boundary contours were found.

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Copyright © 2012