Development of an inverse method using orthogonal basis functions for the evaluation of boundary tractions on an elastic body

Most structural analyses are concerned with the deformations and stresses in a body subjected to external loads. However, in many fields, inverse problems have to be interpreted to determine surface tractions or internal stresses from displacements measured on a remote surface. In this study, the inverse processes are studied by using the finite element method for the evaluation of internal stresses. Small errors in the measured displacements often result in a substantial loss of stability of an inverse system. In order to improve the stability of the inverse system, the displacements on a section near the region of the unknown tractions are predicted by using orthogonal basis functions. We use the Gram-Schmidt orthogonal technique to determine two bases for the displacements on a section near the region of the unknown tractions. Advantages over previous methods are discussed by using numerical examples.