実験計測誤差を最小化する変分原理に基づくモアレ干渉法・有限要素ハイブリッド法 : 弾性変形場の場合

抄録

The authors have previously developed a hybrid method combining the moire-interferometry measurement and the finite element method. This hybrid moire-interferometry and finite-element method made it possible to visualize the stress distribution in a plastic regime. However, the moire-interferometry data often contain the errors associated with the experimental measurement and subsequent fringe analysis. In the present study, first, a variational principle is derived to minimize the errors associated with the moire-interferometry measurement. This variational principle assures also the satisfaction of the equilibrium equation that is one of the governing equations in solid mechanics. On the basis of this variational principle, a hybrid moire-interferometry and finite-element method is developed for the case of elastic deformation field. Concepts of restoration energy and restoration force are introduced. The present hybrid method demonstrates automatic elimination of experimental measurement errors and smooth visualization of stress distribution. Furthermore, the present hybrid method automatically achieves the path independence of the Jintegral, restoring the path-dependence caused by the measurement errors.