# Selection Criterion of Reanalysis Methods for Plane Truss Optimization
###### Abstract  
Structural reanalysis methods have been proposed to improve the efficiency of structural analysis. However, the methods are typically only applicable to their specific type of structural modification. Since the optimization process often involves multiple types of modifications, it is necessary to establish a criterion for selecting the most suitable reanalysis method for each type of modification, aiming to accelerate the optimization process. In this study, the effects of different types of structural modifications are first analyzed. A qualitative correspondence is established between different types of structural modifications and the mainstream of the reanalysis methods. Secondly, the most suitable reanalysis method for different types of structural modifications is quantitatively analyzed from the aspects of selecting efficiency indicators and clarifying accuracy requirements. Finally, in conjunction with the Structural Topology and Shape Annealing (STSA) algorithm, a criterion for selecting reanalysis methods, which are applicable to the optimization process of plane trusses, is established. To verify the validity of the selection criterion, two types of numerical examples are conducted. The results show that the proposed criterion can effectively improve the efficiency of structural computations. structural optimization; plane truss; structural reanalysis method; selection criterion; computational efficiency +
Footnote †: journal: Applied  
0000-0001-4000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-00000-0000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-00000-00000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-000000-0000000-000000-000000-0000000-000000-000000-000000-0000000-0000000-0000000-0000000-00000000-00000000-stiffness matrix and the incremental stiffness matrix. Then the modified structural response can be readily obtained. In recent years, new methods have been developed. [PERSON] et al. [2; 3] proposed a matrix partitioning method named the UMTF method based on the idea of \"filling elements\", which shows good performance in large-scale structural calculations. [PERSON] et al. [4] proposed the Independent Coefficient (IC) method, which simplifies the inputs for the calculation and is suitable for local modification of large-scale structures. On this basis, the more applicable Indirect Factorization Updating (IFU) method [5] has been proposed. In addition, a block-based reanalysis method named the BB method proposed by [PERSON] et al. [6] has been applied to the problem of local modification of large structures. For the processing of sparse matrices, [PERSON] et al. [7] proposed a partial re-decomposition method (PR method) for sparse matrices, whereas [PERSON] et al. [8] developed a method for the rapid decomposition of sparse matrices as a whole. Compared with the exact methods, approximate methods usually estimate the structural response by reducing the solution size (such as reducing the dimension of the stiffness matrix). They can further be classified into four categories: local approximation, global approximation, iterative approximation, and combined approximation [9]. Local approximation methods estimate the structural response based on the calculation information of a single point. The common approach is to perform various series expansions at a single point in order to approximate the exact solution. Typical representative methods include the moving asymptote method [10] and the second-order approximation method [11]. Since these methods only rely on the effective information at a single point, they are suitable for small-scale modifications. Once the modification scale becomes larger, their calculation accuracy may not be guaranteed.