Response simulating interpolation methods for expanding experimental data based on numerical shape functions

Abstract

Abstract An important issue in the existing interpolation methods is that their estimation accuracy usually cannot satisfy the analytical demand to expand experimental data, especially in the case of a few sample points, due to the essential deficiency of physical significance. To address the issue, this study presents an innovative category of interpolation methods which integrates the interpolation with the simulated response characteristics of experimental model. And two specific ones are proposed: the ordinary response simulating method (ORS) and the derivative response simulating method (DRS). ORS takes numerical shape functions simulated by a mechanical model as weighting functions based on general interpolation formula. DRS introduces the simulated model response as a priori estimate of response field, leading to the improvement of interpolation accuracy. Moreover, the two methods are verified through a quasi-real model considering randomness of both load and model defect as well as nonlinearities of material and geometry. It shows that DRS is usually more precise while ORS is more universal as the utilization of model information to different degrees. In sum, both demonstrate their excellent estimation performance and broad development prospects as a new category of interpolation methods.