Partial polar decomposition inverse method applied to determination of internal stresses in an elastic complex structure

An inverse method is developed to evaluate a distribution of internal-stress tractions on an internal surface of an elastic complex structure. The traction distribution is evaluated by measuring a remote displacement field generated when the surface of interest is sectioned. This formulation employs partial polar decomposition (PPD) of a rectangular matrix within the global finite element stiffness matrix for the process of inversion. A systematic regularization process is also provided for the PPD inverse method. This method avoids cumbersome rigid body displacement control required in the formalism of compliance matrix inversion. The method is robust in measuring residual stresses in an elastic complex structure, in particular, multiply connected regions. The inversion method has been tested experimentally by using electronic speckle pattern interferometry (ESPI) with a specimen of multiply connected regions. Experimental results show that the regularized solution using partial polar decomposition converges quickly with a small number of series terms.