My research interests lie in the field of Applied Mathematics and Mechanics, specifically in:

• Elasticity
• Integral Methods of Continuum Mechanics
• Cosserat Solids
• Plates and Shells
• Transmission Boundary Value Problems
• Advanced Composite Materials
• Fracture Mechanics
• Functional Equations Of Continuum Mechanics
• Applied Mechanics And Stochastic Systems
• Structures
• Mechanics & Construction

There is research in progress on both fundamental and applied aspects of the theories of linear elasticity and in the implementation of computational methods for the solution of boundary-value problems arising from those theories. For example, significant progress has been achieved in the investigation of elastic behaviour of advanced materials with significant microstructure, so called Cosserat Solids. This work has found a number of applications in mechanics of composite materials and biomechanics. An interesting direction in the area of Cosserat Elasticity currently under consideration is an application of  the boundary integral equation method to the solution of contact (inclusion, transmission) boundary-value problems. Since the nature of boundary conditions for such boundary-value problems is very complicated and classical methods very often fail to find an adequate analytical solution, transmission problems of Cosserat elasticity may be successfully worked out in Sobolev spaces by means of boundary integral equation method. Such approach has a lot of advantages since it can accommodate domains with irregular boundaries.

In addition, research is being conducted in traditional engineering areas such as plates and shells and inclusion problems of classical elasticity.

Individuals who seek opportunities to work on their graduate degrees and those interested in conducting research in any area of solid mechanics and elasticity are requested to contact Dr. Potapenko directly via email.