The Direct Integration Method for Elastic Analysis of Nonhomogeneous Solids
The direct integration method (a general approach to analysis for boundary value problems of mathematical physics with no implications for the potential functions of higher differential order) is presented in this book as a potential tool for the analysis of the elastic response of arbitrarily nonhomogeneous solids to thermal and force loadings. This method rests upon the correct integration of the local equilibrium equations, which results in an explicit relationship between the stress-tensor components and fundamental integral conditions of equilibrium for individual stresses, which can serve to assure the correctness of the solution and provide a simple verification of computational results. Making use of these relationships and conditions, which are irrespective of the material properties, allows for the reduction of the original elasticity and thermoelasticity problems for nonhomogeneous materials to integral equations of a second kind which implies the solution in a closed form. This feature makes the method efficient for the analysis of arbitrarily nonhomogeneous materials, among which the functionally graded materials are of particular interest for both academia and industry.
Yuriy Tokovyy obtained his PhD in Mechanics of Solids from the National Academy of Sciences of Ukraine in 2003. In 2013, he received his DSc in Mechanics of Solids from the Ministry of Science and Education of Ukraine. His main research interests are direct and inverse problems of thermomechanics of non-homogeneous and thermo-sensitive solids, and analytical and semi-analytical methods of mathematical physics. He published over 220 scientific papers, and is a Board Member of a number of journals
Professor Chien-Ching Ma obtained his PhD in Mechanics of Solids at Brown University, USA, in 1984. In 1985-1989, he worked as an Associate Professor of the Department of Mechanical Engineering of National Taiwan University, and he is currently a Professor at the same institution. His research focuses on solid mechanics, wave propagation and non-destructive testing, fracture mechanics, optical measurement, vibration analysis, and multi-field analysis. He has published over 215 scientific papers.
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