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| A model reduction method based on proper orthogonal decomposition for stiffened shells |
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Abstract Stiffened shells have been widely utilized in the fuel tank and in launch vehicles due to high specific stiffness and strength. Since these structures are subjected to complex dynamic loads, reliable prediction of natural vibration characteristics is essential in preventing excessive vibration levels, which may result in failure or very high noise levels. The natural frequency of a system is calculated via high fidelity model, such as using the finite element (FE) method, however, the detailed FE model has a very high computational cost. In order to obtain frequency of these complex structures accurately and efficiently, reduced order models (ROMs) are used as substitution to decrease the computational expense. This paper presents a model reduction method based on proper orthogonal decomposition technique (POD). The basis idea is to extract the principal component as the transformation matrix from the correlation matrix assembled by nodal displacement field of full order models (FOMs) subjected to different cross-section loads. The relationship between the ability of ROMs to predict mode shapes of interest and cross-section loads is investigated by a clamped-clamped stiffened shell, and the accuracy and efficiency of the proposed model reduction method are also validated by this example. Numerical results show that the maximum frequency error is about 1.01% and the computational time is only 0.03% of the associated FOM. Finally, a free-clamp stiffened shell subjected to harmonic external force is studied and the frequency response function is calculated through FOM and associated ROM. The number of degrees of freedom reduces from 48960 to 480 and average calculation time at each frequency point is only 0.04s for ROM and 4.65s for the associated FOM. And the displacement response in frequency range shows good agreement between the FOM and ROM.
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Received: 04 March 2019
Published: 28 August 2019
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| Fund:;National Natural Science Foundation of China;National Natural Science Foundation of China |
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Corresponding Authors:
Bo Wang
E-mail: wangbo@dlut.edu.cn
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2019, Vol. 40 
