Introduction to Inverse Problems

Abstract

Experimental Stress Analysis has been traditionally applied—through a direct or forward approach—for solving structural mechanical problems as an alternative and complementary methodology to the theoretical one. The great development of numerical methods has largely overruled this task. In addition, the increased accuracy of numerical tools has confined the forward approach to the role of experimental verification restricted to cases of complex and non-conventional numerical modeling, such as stress states resulting from singularities, material anisotropy, etc. If, however, causes (such as forces, impressed temperatures, imposed deformations) or system parameters such as geometry, materials and boundary conditions are unknown, the case is totally different, and the experimental inverse approach has no alternatives. Through measurements of the effects like displacements, strains and stresses, it is possible to find solutions to these inverse problems by identifying the unknown causes, integrating a series of experimental data into a theoretical model. The accuracy of data together with a proper selection of the quantities that must be measured are a necessary premise for limiting the experimental errors that can influence the accuracy of the inversely estimated results.