Material Parameter Identification Of Two-dimensional Orthotropic Bodies By The Boundary Element Method

Orthotropic materials are widely used in modern engineering. Therefore,their material parameters are critical to the design and the evaluation ofengineering structures. These material parameters could be efficientlyevaluated by parameter identification methods, which integrate experimentaltechniques, numerical analysis and optimization techniques. This paperdiscusses some related problems in the parameter identification process forplane orthotropic materials. This process is based on the displacementmeasurement, the Boundary Element Method (BEM) and theLevenberg-Marquardt (LM) optimization method.According to the feature of the fundamental solutions of planeorthotropic bodies, the property of natural logarithm is used to develop thepartial derivatives of the fundamental solutions over each parameter. Based onthese results, the sensitivities of the displacement to the parameters areformulated under the BEM framework. This work lays a foundation for theparameter identification and the corresponding measurement placementoptimization algorithms.Then a parameter identification algorithm is developed for planeorthotropic bodies by the BEM and the LM method. The parameteridentification problem is formulated as the optimization problem ofminimizing the square sum of the differences between the measured andcalculated displacements. In the identification process, the sensitivity analysisis based on the Finite Difference Method (FDM) and the DirectDifferentiation Method (DDM), respectively. Comparing these two methods,it reveals that although the FDM is easy to program, the selection of itsperturbation step is quite empirical, and it is computationally expensive,especially for problems with large number of freedoms;on the contrary, theDDM is not easy to program, but computationally more efficient than theFDM.From the analysis of the well-posedness of the LM method, a criterion ofselecting the measurement placement and an estimation of the maximum biasof identified parameters are deduced. Based on these results, an algorithm forselecting the good measurement placement is proposed and it has been codedinto a computer program. The validity of this algorithm is illustrated by somenumerical examples. These examples reveal that the measurement placementmust be carefully designed, because it has significant impact on theidentification result. Furthermore, an iterative process of selectingmeasurement placement is suggested to minimize the parameter identificationerrors due to the initial rough estimation of true parameters.