Toshiya Nakamura

  Toshiya Nakamura is the Director, Structures and Advanced Composite Research Unit, JAXA since 2018.

1991 PhD in Mechanical Engineering, The University of Tokyo, Japan

1994-2000 Associate Professor, The University of Tokyo

1995-1996 Visiting Professor, Rensselaer Polytechnic Institute (NY, USA)

2011 Head, Airframe Structure Research Group, Japan Aerospace Exploration Agency (JAXA)

2016 Deputy Director, Next Generation Aeronautical Innovation Hub Center, JAXA

His current interest lies on the Applied Elasticity. Especially, on the Inverse Problems in Elasticity and Thermoelasticity, and their application to structural health monitoring.


Reconstruction of Stress Field based on Stress Functions


Recent development of the strain sensor based on optical fiber technology enables one to obtain strain data with high spatial density. The objective of the present study is to reconstruct the stress field from the measured strain data. Since the strain can be measured only along the fiber direction, an inverse elastic analysis is inevitable to reproduce the two-dimensional stress field which has three components of plane stress tensor. Due to the ill-posed nature of the inverse elastic problem, the stability of the analysis strongly depends on the modeling of the displacement and/or load conditions on the boundary, and their degree of freedom.


A trial is made in this study where the stress distribution is deduced from the stress functions. The advantage of using the stress functions is that the stress equilibrium and strain compatibility are automatically satisfied, resulting a sound restriction to the possible solution.


We use the complex stress functions given by the series of analytic functions, then the problem turns to be finding the proper set of coefficient that makes the best fitting to the measured strain data. Numerical examples are presented that are the stress concentration problems around a hole in a plate. It is demonstrated that the present method reconstructs the stress field around the hole and the estimated stress agrees with the FE analysis result.