54.80 Angewandte Informatik
This study is focused on finite element analysis of a model comprising femur into which a femoral component of a total hip replacement was implanted. The considered prosthesis is fabricated from a functionally graded material (FGM) comprising a layer of a titanium alloy bonded to a layer of hydroxyapatite. The elastic modulus of the FGM was adjusted in the radial, longitudinal, and longitudinal-radial directions by altering the volume fraction gradient exponent. Four cases were studied, involving two different methods of anchoring the prosthesis to the spongy bone and two cases of applied loading. The results revealed that the FG prostheses provoked more SED to the bone. The FG prostheses carried less stress, while more stress was induced to the bone and cement. Meanwhile, less shear interface stress was stimulated to the prosthesis-bone interface in the noncemented FG prostheses. The cement-bone interface carried more stress compared to the prosthesis-cement interface. Stair climbing induced more harmful effects to the implanted femur components compared to the normal walking by causing more stress. Therefore, stress shielding, developed stresses, and interface stresses in the THR components could be adjusted through the controlling stiffness of the FG prosthesis by managing volume fraction gradient exponent.
Different types of data provide different type of information. The present research analyzes the error on prediction obtained under different data type availability for calibration. The contribution of different measurement types to model calibration and prognosis are evaluated. A coupled 2D hydro-mechanical model of a water retaining dam is taken as an example. Here, the mean effective stress in the porous skeleton is reduced due to an increase in pore water pressure under drawdown conditions. Relevant model parameters are identified by scaled sensitivities. Then, Particle Swarm Optimization is applied to determine the optimal parameter values and finally, the error in prognosis is determined. We compare the predictions of the optimized models with results from a forward run of the reference model to obtain the actual prediction errors. The analyses presented here were performed calibrating the hydro-mechanical model to 31 data sets of 100 observations of varying data types. The prognosis results improve when using diversified information for calibration. However, when using several types of information, the number of observations has to be increased to be able to cover a representative part of the model domain. For an analysis with constant number of observations, a compromise between data type availability and domain coverage proves to be the best solution. Which type of calibration information contributes to the best prognoses could not be determined in advance. The error in model prognosis does not depend on the error in calibration, but on the parameter error, which unfortunately cannot be determined in inverse problems since we do not know its real value. The best prognoses were obtained independent of calibration fit. However, excellent calibration fits led to an increase in prognosis error variation. In the case of excellent fits; parameters' values came near the limits of reasonable physical values more often. To improve the prognoses reliability, the expected value of the parameters should be considered as prior information on the optimization algorithm.