Correlation aspects of spacecraft and multi-physics finite element models

Abstract

Finite element analysis is widely used to predict the behaviour of complex structures such as spacecraft and/or multi-physics systems. The ‘quality’ of the Finite Element Model (FEM), defined as the capability of the model to simulate the behaviour of the real physical hardware, is assessed by comparing the analytical results with experimental data. In this thesis, Modal Assurance Criterion (MAC) and Normalised Cross Orthogonality (NCO) check are examined for their usefulness in the correlation of real spacecraft structures and then applied to multi physics systems using the results of the ‘true’ FEM as the experimental or nominal data and those obtained from the erroneous FEM as analytical data. The NCO check requires a compatible mass matrix, which can be obtained from the global or complete FEM using the System Equivalent Reduction Expansion Process (SEREP). Here, a probabilistic approach is used to assess the robustness of a SEREP based test analysis model to inaccuracies by inputting a range of known errors into the modes of three spacecraft models. The effect of parameters used in the SEREP and the degree of inaccuracy tolerated in the modes before failing the NCO check were examined. The relationship between the capability of the FEM to predict some relevant responses and the quality of the model correlation determined using MAC and NCO check was also investigated. A method to optimise the choice of accelerometer locations to increase the robustness of the NCO check is proposed. In addition, the effectiveness of MAC and NCO criteria in the prediction of structural response under the base excitation was performed using three spacecraft models. It is observed that these criteria are not entirely satisfactory, particularly when the FEM is used to predict the forced response characteristics. A qualitative indicator termed the Base Force Assurance Criterion (BFAC) is then defined by comparing the nominal dynamic force at the base and the FEM predicted base force to predict the possible error in the peak acceleration and the dynamic displacement. The results show that the BFAC can better correlate the response than the conventional MAC or NCO check. The correlation of the FEM of two types of multi-physics systems, namely viscoelastic damped systems and a piezoelectric system were also carried out. The usefulness of MAC and NCO check in the prediction of loss factor of the viscoelastic systems is assessed and it is noted that these correlation methods fail to represent the dynamic characteristics under base excitation and once again, the BFAC is found to be a better tool to correlate the viscoelastic systems. The effect of temperature as an uncertainty on the MAC and NCO check is also studied using the viscoelastic systems. The usefulness of the MAC for the correlation of the FEM of a shunted piezoelectric system is also analysed under the harmonic excitation. It is observed that the MAC has limited use in the correlation of such systems. Finally, a new correlation method based on electric current is defined and it is shown that this criterion correlates the dynamic characteristics of the piezoelectric system better than the MAC.

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