Analyses of inverse problems arising in the field of mechanics and strength of materials are reviewed. The inverse problems are defined as the problems dealing with the estimation of input from output. Based on this definition the inverse problems can be classified into boundary/domain inverse problems, governing equation inverse problems, boundary value/ initial value inverse problems, force/source inverse problems, and material properties inverse problems. It is noted that the inverse problems are usually ill-posed: they lack in existence, uniqueness or stability of the solution. Representative schemes for the solution of the inverse problems are introduced with special emphasis on regularization. Examples in these categories of inverse problems and their analyses are shown. Successful use of the regularization methods in the analyses are described. It is shown that subsidiary information, such as a priori knowledge and fundamental laws, can be successfully used for improving the mathematical structure of the ill-posed inverse problems and obtaining good estimates.
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