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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 serv.