Research On Rapid Reanalysis Methods Of Structural Modes

With the progress of science and technology, industrial structures are beingdeveloped towards the large-size and great complex. Excellent performance and higheconomic utility of the large-scale structures in many engineering fields includingaerospace, automobile and civil engineerings etc. are required, and the designs andoptimizations for such large-scale structural systems become more and morecomplicated. The rise of computer technology and the advancement of CAEtechnology make design and optimization of the large-scale and complex structurepossible. However, as the design scale becoming larger and design parametersbecoming more, traditional optimization method will consume huge computationaltime, especially in reanalysis process and can not meet the practical needs any more.Many scientific and technological workers are thus paying their attentions to seekinga faster computational method for structural reanalysis.Several reanalysis methods for the modal reanalysis problem of structuralmodifications, including Subspace Iteration method, Combined Approximationsmethod which is referred to as the CA method are first summarized. At the same time,the Gram–Schmidt orthogonalization of the basis vectors for approaching modeshapes is introduced, which can improve the accuracy of the solution. A new methodfor fast mode reanalysis is then presented. It is based on CA method and recombinesthe basis vectors of reduced subspace calculated by CA method, the purpose of which is to obtain all the eigenpairs requested in one reduced subspace withoutcalculating the eigenpairs one by one as CA method. Thus, the new method can solveall the requested eigenvalues and eigenvectors without using Gram–Schmidtorthogonalizations of the basis vectors and avoids the error accumulation. Thecomputational effort needed by new method is usually much smaller than thoseneeded by Subspace iteration method and CA method. Moreover, the new method isstraightforward, which can be readily used in structural reanalysis. Because the basisvectors of the reduced subspace are achieved by Taylor series expansion, theefficiency of the calculations and the accuracy of the results can be controlled by theinformation considered. Efficient solutions can be achieved by low-orderapproximations and accurate results are obtained by adding higher-order terms.In this paper, the modal reanalysis method with unchanged degree of freedom isstudied and discussed. In order to demonstrate the accuracy and efficiency of thenew method, three numerical examples are presented. The accuracy of numericalresults and computational times are compared for the present method and the CAmethod. Three numerical examples show that, both in terms of accuracy and savingcomputational time, the new approach are better than the CA method. Especially forthe modal reanalysis of large-scale structures, the superiority of new method is muchmore obvious.