结构参数大修改时的特征值重分析方法

就结构参数发生大修改的情况提出了两种高精度的特征值重分析方法：Ｐａｄｅ　逼近法和推广的Ｋｉｒｓｃｈ混合法．利用这两种方法，计算了一个具有２０２个结点，３５７个梁单元的平面框架的近似特征值．计算结果表明，所提出的方法是结构参数修改时的特征值重分析的有效方法．

EIGENVALUE REANALYSIS METHODS FOR LARGE MODIFIED STRUCTURES

In the optimization of structural systems, it is very important to compute the eigenvalues of the structures when the parameters of structures are made. In many cases, one of the main obstacles is the high computational cost involved in the solution of large-scale problems. Application of approximation methods in structural optimization is intended to reduce the com- putational cost. In general, the following factors are considered in choosing an approximate model for a specific optimal design problem: (1) the accuracy of the calculation; (2) the efficiency of the method; and (3) the ease of implementation. At present, the various approximations can be divided into the following cases: 1)the first class is global approximation(also called multipoint approximation), such as polynomial fitting or reduced basis methods. These approximations are obtained by analyzing the structure at a number of design points, and they are valid for the whole disign space; 2) the second class is local approximation (also called singlepoint approximation), such as the first-order and second-order Taylor series expansion about a given point in the design space. Local approximations are based on information calculated at a sigle point. These methods are effective only in cases of small changes in the structural parameters; For large changes in the design, the accuracy of the approximations often deteriorates, and they may become meaningless; 3) the third class is the combined approximation presented by Kirsch, which attempts to give global quality local approximation. The advantage of this approach is that, similar to local approximations, the solution is based on results of a single exact analysis. To preserve the ease of implemention and the efficiency of the common perturbation method and improve significantly the quality of the results, for the case of the large modification of the structural parameters, two high-accuracy eigenvalue reanalysis methods, i.e., Pade approximate method and extended Kirsch combined method, are presented in this paper. The proposed methods are used to calculate the approximate eigenvalues of a plane frame with 202 nodes and 357 beam elements. The results show that the proposed methods are efficient in the eigenvalue reanalysis when large modifications of the structural parameters are made.