Mathematical modeling and computer analysis of physical processes of different nature in applied problems


Numerical modelling and software development for creep-damage processes in structural elements

Numerical modelling of creep and damage accumulation processes in structural elements and devices, which are subjected by complex action of cyclic loading and heating, can be done by use of developed software which include FEM programs for 2d, 3d problems and thin shells of revolution. Non-stationary heat expansion 3d problem is solved additionally. Original pre- and postprocessors are available.

Novelty and benefits. The developed approach for cyclic loading and heating in creep-damage conditions has been presented and published in scientific journals. One part of the project was awarded by CEGB prize (UK). Developed software was used for design and long term strength analysis of different structural elements and devices of turbines as well as space- and aircrafts.

Outlook and perspectives:

  • Development of new commercial version of software
  • Joint projects directed to estimation of long term strength of structural elements


Probabilistic modeling of structural failures for a prediction of mechanical engineering elements reliability

The work deals with a problem of the development of computational methods of determination of mechanical engineering elements life-time with random material characteristics and load. It is offered improved probabilistic models of the fatigue damage accumulation in the materials under cyclic deformation with finite strain amplitudes in the framework of continuum damage mechanics. The appropriate models take into account a random scatter of the material fatigue resistance characteristics, along with simultaneous passing of stochastic processes of material properties degradation caused by natural aging. The approaches are developed for the determination of the probability characteristics of the machine elements fatigue damage and lifetime considering the presence of possible operational random variation of the characteristics of the deformed state.

Outlook and perspectives:

  • Analysis of the reliability of the elastomeric materials subject to the estimation of the influence of the self-heating process (the modelling of the self-heating of the elastomeric material under the cyclic load, analysis of cyclic heating of elastomers on their aging process)
  • Development of the computational approaches for the estimation of the reliability of engineering designs considering simultaneous corrosion defects stochastic growth, material chemical degradation and the process fatigue accumulation


Biomechanical computer-aided design and modeling

Theoretical (i.e. computer analysis (CAE)) of the stress state and deformation of biological bone tissues themselves and together with fixing system or implants require the development of complicated mathematical models.  The main challenges here are following: complicated 3D geometry of the bone; multilayered internal structure; curvilinear orthotropy of the properties; nonlinearity of the mechanical behaviour; identification of material properties for a living tissue; specificity of the properties, geometry and loads from patient to patient; and implementation of new bio-neutral composite, functional and smart materials.

Outlook and perspectives:

  • the methods for parametric modeling of fixation devices and their installation based on computer tomography data that will enable adaptation to specific clinical cases;
  • new rheological models of materials reflected the heterogeneity of bone structure, anisotropy of mechanical properties.
  • automated software systems oriented on general usage of computer-aided design in medical practice by a staff of clinical centers orthopedics and traumatology


Oleksiy Larin – Director of Institute Of Education and Science In Engineering and PhysicsProfessor, Doctor of Technical Sciences:

Olena Slipchenko – Director of European Educational Scientific Technological Center – Ph.D. in technical sciences, Senior Researcher: