I. | FIRST STAGE | ||
No of stage | Content of the stage and planned activities | Duration of the stage and concrete activities (months) | Expected results |
1 | Investgation of mechano-mathematical models describing the processes in 2D cracked piezoelectric materials subjected under coupled dynamic loads using hybrid approach based on elastodynamic and dynamic fracture mechanics. | 12 | Solution of the direct problem and simulation studies for the sensitivity of the Stress Intensity Factor near the crack-tip to the input data and parameters of the used mechanical models. |
2 | Formulation of the problem describing Reaction-Diffusion Cellular Neural Network models for the crack identification in piezoelectric materials. | 12 | Solution of the inverse problem and validation of the results for identification of the geometrical and mechanical crack’s characteristics in piezoelectric materials. |
3 | Applying the non-hypersingular traction based Boundary Integral Equation methodology for solution of the proposed models and evaluation of the fracture state of cracked in-plane or anti-plane finite piezoelectric solids under combined electro-mechanical dynamic load. | 6 | Evaluation of the accuracy and validation of the theoretical and numerical tools for solution of the direct and inverse problems on the base of the existing test examples. |
4 | Investigation and development of different Cellular Neural Network models based on discrete schemes, study the properties of the solutions and the corresponding Cellular Neural Network’s. | 6 | Obtaining of analytical and numerical solutions for different Cellular Neural Network models. |
5 | Preparation of publication of the obtained results in scientific journals on Applied Mathematics and Mechanics and on Applied Informatics. | 18 | Publications and reports of the obtained results. |
6 | Development of the website of the project with on-line computational tools. | 18 | Internet website of the project. |
II. | SECOND STAGE | ||
No of stage | Content of the stage and planned activities | Duration of the stage and concrete activities (months) | Expected results |
1 | Development of the numerical schemes and computational tool for solution of the posed problems. | 6 | Validated scientific software. |
2 | Interpretation of the obtained results and implementation of the derived algorithms on a Cellular Neural Network -based architecture which represents a novel computing paradigm. | 6 | Algorithm for identification of the crack parameters (length, location, Stress Intensity Factor) with Cellular Neural Network, using data by the Boundary Integral Equation Method solution of the direct problems. |
3 | Simulation study for different boundary value problems describing different scenarios of cracked finite homogeneous and inhomogeneous piezoelectric solids subjected under electro-mechanical dynamic loads. | 12 | Parametric studies using data for existing piezoelectric materials with cracks. |
4 | Preparation of publication of the obtained results in scientific journals on Applied Mathematics and Mechanics and on Applied Informatics. | 18 | Publications and reports of the obtained results. Presentations of the obtaining new results concerning models, methodology, solutions and their application on scientific seminars and conferences. |
5 | Managements and support of the website. | 18 | Useful internet product as for information’s aim so for educational aim directed to MSc and PhD students. |
The research projects and programs of IMI have been carried out in a close collaboration within Bulgarian and international joint scientific teams...
Institute of Mathematics and Informatics
Institute of Mechanics
New Bulgarian University
National Science Fund
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