Institute of Mathematics and Mechanics

Azerbaijan National Academy of Science

27/06/2014

**Basic scientific achievements**

- The effective theory of deformation and destruction hereditarily (visco) elastico-plastic bodies under arbitrary (including cyclic) loads is worked out.
- The effective method of discount of temperature influence onto mechanical propoties hereditarily (visco) elastic materials is worked out. It was proved the theorem, reducing solution of common problem thermo-viscoelasticity to solution corresponding usual visco-elasticity problem by using this method.
- The effective theories of long strength hereditarily elastic (visco) bodies and cyclic strength (tiredness) of elastico- plastic bodies are developed; d) the simulation of long destruction process is constructed.
- The simulation of long destruction process is constructed;
- The method of solution of common boundary value problem of elastico-plasticity by simplification is offered.
- The effective method of proximate solution of general problem of linear visco-elasticity theory is offered; the exact analytical form of well-known A.A.Ilushin experimental function, using in the approximation method is defined.
- There are produced the calculation of strength of different constructions, including rockets with hard fuel under the dynamical temperature load operation.
- The effective spectral theory of non-regular(random) waves, which are in application to sea waves allowed to find the pressure of wave in any depth and other parameters of sea waves is offered.
- The effective theoretical-experimental method is worked out. It allows to define the time up to corrosion destruction of arbitrary geometry constructions, which are worked out under mechanical stress in aggressive medium.
- Analogical method, permitting to forecast the time up to corrosion destruction of tiredness destruction is offered.

11. There was offered formula, defining the life of construction of arbitrary geometry, subjected to random loads.

12. A mathematical model of icing process on the surface of aircrafts during the flight has been founded.

**The list of publications at the 5 years published**

- Nonlinear theory of thermal stresses in viscoelastic bodies//Mechanics of composite materials. 1983, v.19, №4, p.419-425.
- Deformation of a viscoelastic cylinder fastened to a housing under non-isothermal dynamic loading. PMM Journal of Applied math. and mech. Engl.tr. 1990, v.54, №1, p.74-82
- К вопросу деформирования и разрушения вязкоупругих тел при наличии температурного поля. Изв. АН СССР. Механика твердого тела, 1990, №2, с.127-139.
- Modeling of fatigue fracture under stationary stochastic loading conditions. Applied Math. and Computation. 2007, v.184, p.874-879.
- Boussinesq’s viscoelastic problem on normal concentrated force on a half-space surface. Mech. Of time-depend mater. 2010, v.14, №3, p.253-259.