Reconstruction of eigenstrains and residual stresses in thin plates from modal sensitivity analysis

Non-destructive evaluation of the spatially resolved residual stresses from limited measurement data is crucial for a comprehensive assessment of structural integrity and performance reliability of engineering components. Generally, residual stresses are caused by incompatible internal eigenstrains and along this line, a novel sensitivity-based eigenstrain reconstruction approach is developed in this work for residual stress identification in thin plates using vibrational modal data. There are two key ingredients in establishing the proposed approach. At first, residual stresses are parameterised through direct eigenstrain analysis and thereafter, residual stress reconstruction is recast as a parameter identification problem whose goal function is just the least-squares of the misfit between the measured and calculated data. Second, to minimise the nonlinear least-squares goal function, the modal sensitivity analysis is called to linearise the misfit and the trust-region constraint is invoked in conjunction with the Tikhonov regularisation to enhance the convergence. Numerical examples are investigated to verify the robustness, accuracy and efficiency of the proposed approach.