Smoothing Measured Displacements and Computing Strains Utilizing Finite Element Method

A method for smoothing measured displacements and computing strains utilizing a finite element method is proposed. Nodal displacement values of a finite element model are determined by fitting the interpolation functions of finite elements to measured displacement values using the method of least-squares. Then, the smoothed displacement distributions are obtained. The displacements in the region where the measurement values are not obtained or unreliable are determined by solving finite element equations. The validity is demonstrated by applying the proposed method to displacements of a plate with a hole obtained by finite element method. Results show that the displacements and the strains can be determined accurately by the proposed method. Furthermore, the strains near free boundaries can be determined easily. As strains can be evaluated easily and accurately, it is expected that the proposed method can be applied to various problems in solid mechanics.