Recent Advancements in the Elastic Analysis of Nonhomogeneous Structures: Direct in Integration Approach



报告题目:Recent Advancements in the Elastic Analysis of Nonhomogeneous Structures: Direct in Integration Approach

报告人:  Prof. Yuriy TokovyyNational Academy of Sciences of Ukraine





Nonhomogeneous materials and structures (the ones exhibiting spatial variation in mechanical and thermo-physical properties) are widely used in current technology. The growing interest to the theoretical analysis and practical implementation of such materials are particularly induced by the widespread application of the functionally graded materials (FGM), whose nonhomogeneous properties can be formed technologically in order to gradually change the properties from one surface to another.  Introduction of an FGM intermediate layer, for instance, allows for the achievement of required operational performance by reducing the residual stresses arising due to the mismatch of the dissimilar characteristics of neighboring layers (for example in ceramic-metal composites). However, introduction of the material nonhomogeneity into the mathematical models of relevant mechanical problems delivers considerable difficulties into their mathematical treatment by either analytical and numerical means, which affects the accuracy of analysis significantly.  This calls for further development of the existing models and methods as well as introduction of the new ones.

This talk addresses the recent advancements in the elastic analysis of nonhomogeneous materials and structures with special attention given to a novel approach based on the direct integration method. The central idea of this method is to reduce the original problems to the governing equations on the basis of the compatibility conditions in terms of stresses accompanied with appropriate boundary and integral conditions, which can be established by the integration of the equilibrium equations. For nonhomogeneous materials, the mentioned governing equations appear in the form of integral equations of second kind. The solutions to the latter equations can be achieved by means of either analytical or numerical techniques developed within the framework of the integral equations theory. The basic features of this method consist in

i) the applicability to the analysis of arbitrarily-nonhomogeneous solids and

ii) the universality of its application for the domains of different shape related to different coordinate systems.


Prof. Yuriy Tokovyy (doctor of physical-mathematical sciences, senior scientific researcher) is a specialist in the fields of mechanics of deformable solids, thermoelasticity, and mathematical modeling. His results are presented by over 200 scientific publications, the majority of which are published in high-rated international journals.

He is a dean of the department Solid Mechanics in the Pidsrtyhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine (Lviv, Ukraine). In 2003, he gained his PhD in mechanics of solids at the National Academy of Sciences of Ukraine. In 2013, he received his Doctor-in-Sciences degree from the Ministry of Sciences of Ukraine. In 2012 – 2013, he was serving as one of the section editors of the “Encyclopedia of Thermal Stresses” (Springer, 2014) – the largest scientific publication devoted to subject of thermal-stress analysis that has been ever published. He is a member of the Editorial Boards of the scientific journals “Mathematical Methods and Physico-Mecanical Fields”, “Applied Problems of Mechanics and Mathematics”, “Bulletin of the Donetsk National University: Physico-Mathematical Sciences”, “Mechanics of Composite Materials” and was promoted to become a member of the Board for the “Journal of Thermal Stresses”.

His main research interests are concerned with the direct and inverse problems of mechanics of deformable solids, thermomechanics of nonhomogeneous and thermosensitive (FGM) solids, analytical and semianalytical methods of mathematical physics.

Yuriy V. Tokovyy has published over 200 scientific papers, a number of critical reviews and encyclopedia essays.