Study On Dynamic Model Reduction And Optimization Of Complicated Slender Structures

In modern engineering calculations, we often have to deal with dynamic analysis, or even optimization of dynamic performance for complicated slender structures, such as rockets, railroad cars, ships and high-rise buildings. With the development of CAD technology and finite element preprocessor, FEM model with huge number of degrees of freedom is often easily constructed and used for static analysis of such complicated structures. However, due to time-consuming computations and huge storage requirement of dynamic analysis and optimization, it is almost impossible to optimize structural dynamic performances based on the model which has huge number of degrees of freedom. Therefore, based on the fine FEM model of such complicated structures, constructing an approximate physical model with a small amount of work, which can be used to predict the structural dynamic performance and meet the requirement of design, optimization, simulation and other tasks in the preliminary design stage, is still very valuable in many design departments. To meet the need, the present work starts from the summary of dynamic model reduction methods and completes the following study:1. The reduction method based on the assumption of block-wise rigid body motion is further modified and studied. By considering the rotational freedom of the original structure, the displacement transfer matrix is modified and the method is used for model reduction of complex spatial structure, two examples show the effectiveness of the modified method in this paper. By combining the reduced model with the variable decomposition approach, an efficient dynamic optimization method based on reduced model was developed. Then two optimization model are established, in which the constraint to keep the structural mass constant is imposed, the shell thickness is design variables, and the optimization objective is to maximize the fundamental frequency of the original structure and the frequency gap between the first two consecutive vibration frequencies respectively. By comparing with optimization based on response surface model and original model, the results show that the optimization based on the reduced model has high computational accuracy and efficiency.2. By using the modified reduction method which is based on the assumption of block-wise rigid body motion, a physical reduced model of a large complex space truss is established. LQG optimal control law is designed to achieve the purpose of a truss structure vibration active control based on the physical reduced model. By comparing with the internal balanced model reduction method, the numerical simulation results show that the physical reduced model not only has higher computational efficiency, but also has higher control efficiency.3. A new model reduction method is presented for the structures whose longitudinal dimension is significantly larger than transverse one. Based on the plane section assumption of the beam theory, the displacement of FEM nodes in each cross section is approximated by the motion of centroid of the cross section through the displacement transformation matrix, resulting in the localized base vectors. When the structure has large openings, structures’cross-sectional warping deformation mode is obtained by using numerical methods, which is considered as additional reduced base vectors. Then a free-free reduced model with high accuracy is constructed. Based on the reduced model, optimization model to minimize the structural weight considering frequency constrain in a variety of boundary conditions is studied. Numerical examples demonstrate the effectiveness of the proposed method.4. The model reduction method based on plane cross-section assumption is further improved by including displacement interpolation function of beam and constructing a new physical reduced base vectors. This improvement solves the deficiency of the model reduction method based on the plane cross-section assumption, such as restrictions on regular finite element grid and large size of the reduced model, and makes the method applicable for more complicated FEM models of arbitrary meshes and geometry. By using the vibration modal vectors of the reduced model and constructing an initial guess of vibration modes of the original structure, one Rayleigh-Ritz iteration results in the vibration frequency of high accuracy. The method is compared with the Krylov subspace method, the examples show the validity and efficiency of this method. Transient dynamic analysis of a complicated example structure is carried out, the results show that the method meets the accuracy of practical engineering and greatly reduces the computational cost.5. Based on the presented model reduction method, slender structure is divided into several beam part and each part is reduced to a super beam element, resulting in a free-free reduced super beam model. The shear deformation is included to modify the super beam for improving computational accuracy. A shear correction factor is quickly calculated or obtained through an optimization process. The numerical examples demonstrate the feasibility and efficiency of the proposed super beam model for fast approximate frequency analysis of complicated slender structures. Examples of specific grid stiffened cylindrical shell model are given to compare the reduced super beam model with the beam model based on equivalent thickness, the static response and equivalent stiffness. Different length, nonuniform structure models are tested. The frequency analysis results show that the reduced super beam not only has high computational accuracy and efficiency, and can handle different situations for a wide range.At the early stage of this dissertation, author attended to the optimization study for aluminum alloy structure of CRH train and published one conference paper. For its difference to the main work of this dissertation, it will be presented in the appendix.