Model Reduction Method For Dynamic Anslysis And Its Application Based On Deformation Modification And Substructure Method

Engineering structures such as high-rise buildings, bridges, tunnels and stadiums are becoming more and more complex. It is hard to describe the performance of complex structures from structural mechanics concepts. With the development of finite element method and computer aided engineering, creating a complete model of the complex structure becomes possible. However, the establishment of a complete computational model requires a lot of effort and storage space. It is very difficult to carry out a stuctural dynamic analysis based on this complete computational model, let along dynamic optimization and reliability analysis. Therefore it is urgent to balance between the accuracy and the simplification and to get a model describing the structural dynamic characteristics accurately enough, whereas with relative small computational burden. Accordingly, this article proposed a method to obtain reduced modelfrom the accurate finite element model and then studied the reduced model’s dynamic characteristics. Stuctural dynamic optimization and reliability analysis based on this reduced model are also carried out. The following contents are included:1. Give the details of the structure modal analysis method and the model reduction method based on deformation modification. ANSYS modal analysis method and the way to output mass and stiffness matrices are introduced. MATLAB is used to read-in the mass and stiffness matrices and excute the modal analysis. A reduced model is then obtained though the deformation modification. Then the reduced model’s frequencies are calculated and several examples show its validity and efficiency.2. Propose a new simplification method—the substructure deformation modification method. Using the the substructure module in the ANSYS and combined with the deformation modification method, a complex structure is simplified to get a reduced model. Four examples show that the simplification models remain dynamic characteristics of the previous complex structures.3. Establish dynamic optimization problems based on the reduced models through the variable decomposition method. Taking beam elements and shell elements as examples, analyze the characteristics of the mass and stiffness matrices. Find the design variables’ influence on the reduced model and establish dynamic optimization problems. Several examples prove the efficiency and correctness of the proposed method.4. Excute structural dynamic characteristic reliability analysis based on the reduced model. Using the geometric meaning of the structural reliable index, the reliability analysis is turned into an optimization problem. Calculate the reliablity index using several optimization methods and compare the results with the results of Monte Carlo simulation. The accuracy and efficiency of the proposed method is proved.