Computational Mechanics Laboratory

Name of the project: Models, algorithms and software tools for multi-scale analysis of new materials and physically active media

Strategy for Scientific and Technological Development Priority Level: а

Project objective:

1) Development of efficient numerical methods and solvers for systems of linear equations; for problems related to eigenvalues; for incorrect problems in application to finite-element matrix problems that are characteristic, predominantly, of problems of piezoelectricity.

2) Development of multi-scale mathematical models with allowances made for dimensional factors, micro- and nanostructure of active and composite materials including those with special boundary conditions on interphase boundaries; techniques of solution of related physical-chemical problems and problems of nanomechanics based on methods of finite element methods and research-intensive software tools; research of problems of piezoelectricity, mechanics of active composite materials, adaptive materials, functional gradient materials, various nanostructures (nanotubes, nanofilms, nanorods) and thin coatings.

3) Development of new relevant models of deformation and oscillations of construction and active materials.

4) Development of efficient procedures for identification of variable characteristics of bodies made of construction and active materials in the light of a preliminary stress-deformed state and nonlinear elastic properties within the ideology of non-destructive control.

5) Development of a library of key elements and new finite-element software complexes with capabilities of computation of physical-chemical problems and modeling of new nano-, active and composite materials, computation of direct and revers problems, with means of optimization, with enhanced means of prepocessor and postprocessor processing, with efficient solvers and parallel computation capabilities.

6) Development of a gridless method of particles with finite-differential and finite-element methods for a computational hydrodynamic experiment to investigate multi-scale structure of flow. Application of the gridless method to flows of ideal and viscous liquids in semi-bounded regions. Development of fast numerical methods of matrix-vector analysis of ultra-high dimensionality. Applications to computation of statistical characteristics of turbulent flows at high Reynolds numbers. Building and implementation of new computation algorithms inheriting properties of equations of hydrodynamics, in particular, multistability and formation of continuous families of solutions.

7) Implementation of results of scientific research into master degree programs «Fundamental mathematics, mechanical engineering and mathematical modeling», «Computer mathematics: theory and applications», «Mathematical Modeling and Informational Technologies» (Mathematical modeling and information technologies, program in Enginsh), and in the program of training of scientific and pedagogical staff in the postgraduate school in the training directions corresponding to specializations 01.02.04 «Mechanics of deformation of deformation of solid bodies» and 05.13.18 «Mathematical modeling, numerical methods and software complexes», training of highly qualified staff in the domain of the project.