Nicholas M. Bessonov
E-mails: bessonov@bess.ipme.ru (or nbessonov@hotmail.com)
Research and development work in computation mechanics. Development of an original vector finite difference (VFD) method. The VFD method conserves compact vector-tensor notation (the natural language of continuum mechanics) from mathematical formulation, through numerical scheme, and programming code. As a result (in comparison with traditional technology) the two last steps are significantly simplified, especially for multi-dimensional problems in the regions with complex constitutive relationships and (or) irregular geometry. So more attention can be focused on physical part of problems (details).
Object-oriented languages like C++ or Fortran90 allow to develop new data types (classes) for vectors-tensors variables which encapsulated all features of vectors-tensors calculus and greatly simplifies programming code.
VFD pioneered in simulating of 4D-space continuum problems
Selected applications:
Problem: Simulation of a bullet penetrating an aluminum plate. |
Model: 2D, unsteady, elastoplastic media with hardening, fracture media, mild contact algorithm. Numerical method: explicit VFD. Programming language: Microsoft C++ |
Problem: |
Model: 3D, unsteady, hyperelastic media, simple contact algorithm. Numerical method: explicit VFD. Programming language: Borland C++ |
Problem: Knot simulation. |
Model: 3D, steady, hyperelastic media, advanced contact algorithm. Numerical method: Implicit VFD. Programming language: Borland C++ |
Problem: Dynamic hyperelastomer simulation. |
Model: 3D, unsteady, hyperelastic media. Numerical method: Implicit VFD. Programming language: Borland C++ |
Problem: Deformation of a car (Impact simulation). |
Model: Unsteady, shell elastoplastic structures with hardening, fracture media, mild contact algorithm. Numerical method: Implicit VFD. Programming language: Microsoft C++ |
Problem: Bound rubber tube (different stationary solutions). |
Model: 3D, unsteady, hyperelastic media. Numerical method: Implicit VFD. Programming language: Borland C++ |
Problem: Thermo-convection in a closed space. |
Model: 2D, unsteady, viscous fluid. Numerical method: implicit VFD. Programming language: Microsoft C++ |
Problem: Dynamic cutting of metal simulation |
Model: 2D, unsteady, elastoplastic media with hardening, fracture media, friction model, mild contact algorithm. Numerical method: implicit VFD. Programming language: Microsoft C++ |
Practical proof of the performance of the VFD.
Increasing problem dimensions (1D, 2D, 3D) increase programming efforts in many times. The listing of the "numerical" part of computer program based on VFD for 4D space include less than 200 lines and increase less than 40% in comparison with 3D case (based on VFD technique too). Most of 3D program is re-usable (details).
We can not show the 4D-space hyperelastic solid after deformation. Nevertheless we can show its 3D cross-sections and 3D shadow (below):
Problem: 4D-space solid deformation (details). |
Model: 4D-space hyperelastic media. Numerical method: Implicit VFD. Programming language: Borland C++ |
Development of the theory of liquid with microstructure and its application to analysis of filtration, lubrication, flow of suspensions and similar problems. The generalization of the classical theory of viscous liquids to micropolar liquids (those with microstructure).
Development of micropolar lubrication theory in submicron channels based on with anomalies near solid surfaces (List of Selected Publications).
Publications: Published one book (co-author) and more 60 than papers in Russian journals.
Current Position: Lead Researcher
Address: Institute of Problems of Mechanical Engineering Russian Academy of Sciences
V.O., Bolshoj pr., 61, St. Petersburg, 199178, Russia.
Phones: +7(812)321-47-64
Fax: +7(812)321-47-71
E-mails: bessonov@bess.ipme.ru (or nbessonov@hotmail.com)
Key Worlds: numerical simulation, continuum mechanics, vector-tensor calculus, finite difference, finite volume, object-oriented programming.