The following PhD programs are proposed in connection with the scientific program of the project:

 

1. Mathematical modeling ane numerical solution of coupled mechanics problems in domains with singularities.

 

Summary.

The solution of Boundary Value Problems (BVP) elastic systems in domains with cracks, cavities, nonhomogeneities is applied in problens of Fracture Mechanics, Seismic Mechanics ect. Perespective numerical method in the last years is Boundary Integral Equation Method (BIEM). In order to apply this method we have to study BVP for partial differential equations, derivation of fundamental solution or Green's function and obtaining the corresponding to BVP integrodifferential equation on the boundary of the domain. The numerical solutions needs to be studied for sccuracy and convergence and validated with benchmark examples.

The educational part of the PhD study is concentrated on eliptic and hyperbolic partial differential equations in domain with singularities and corresponding BVP, the theory of integrodifferential equations, mechanics of continum media, modelling of cracks and other inhomogeneities, application of BIEM, programing with Mathematica and Matlab.

The aim of the PhD study is otaining new theoretical results for solution of couple problems with application in Fracture Mechanics and Seismic Mechanics.

Prof. DSc Tsviatko Rangelov, Department of Differential Equations and Mathematical Physics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, еmail: rangelov@math.bas.bg

 

2. Mechanical modelling of cracked piezoceramic composites under dynamic excitation

 

Summary.

After the discovery of the Curie brothers (1880) of the piezoelectric effect, the idea of entering the multifunctional in nature materials in people's lives and in industry is in its latent period. However, after the Second World War, after the ferroelectric materials discovery and on their basis the creation of ceramic composites with very strong electro-mechanical properties, the picture changed dramatically. Today, their intensive penetration into areas such as medicine (piezo-surgery), automotive, aviation and transport industries, electronics and computer industry, telecommunications, scientific instrumentation, modern technologies of current intelligent structures is a fact. The priorities of world research centers in the USA, Germany (Max-Planck, Fraunhofer Institutes) and Japan are the study of the mechanical properties of structural piezo-elements (sensor, actuator) and the assessment of their reliability and integrity when they contain different type of defects such as cracks, cavities, elastic inclusions and are under different type of electro-mechanical loads. During the operation of these structural elements, the presence of defects can lead to damage and destruction of the respective piezoelectric element, but through it to the destruction of the entire engineering system. This requires the study of the behavior of these materials under the influence of different types of electro-mechanical loads, taking into account the presence of different type of defects in them. The mechanical models will take into consideration the material anisotropy, the existence of material gradient and the size of the defects under consideration.

The educational part of the PhD program includes accumulation of in-depth knowledge of mechanics of continuous media, fracture mechanics, computational mechanics, material science, mathematical physics, method of boundary integral equations as basic numerical tools, advanced programming, usage of Mathematica, Matlab, mechanical and physical interpretation of the obtained results, their presentation and participation in scientific forums at home and abroad. Cooperation between Institute of Mechanics and Institute of Mathematics on the proposed topic has existed for 15 years, within projects funded nationally and internationally.

Prof. Dr. Petya Dineva, Institute of Mechanics, BAS, e-mail: petia@imbm.bas.bg