Research On Fast Algorithm For Structural Vibration And Control Based On Dynamic Explicit Formulation

With the continuous development of science and technology, engineering structures are becoming increasingly complicated:on the one hand, the scale is larger and larger, such as high-rise buildings, large span bridges and huge launch vehicle, etc.; on the other hand, the composition is more and more complex, for example, a lot of new materials have been widely used. As infrastructures and public facilities, the safety and reliability of the above engineering structures in the process of operation are directly related to people’s life and property safety, which require extra attention:dynamic analysis should be carried out on the structures to determine the vibration response under dynamic load; in the meanwhile, necessary control should be applied on the structures to suppress the harmful vibration. However, due to the large-scale and complex composition of the structures, it is sometimes difficult to carry out an efficient and accurate numerical simulation by traditional methods. Therefore, the research on fast algorithms for vibration and control analysis of complex structures is of great significance.Based on the motion’s essence of linear structural system and time integration methods, this dissertation gives a general expression of the dynamic response for linear structural system-dynamic explicit formulation. Dynamic explicit formulation takes the influences of both initial disturbance and external load on dynamic response into account and expresses the dynamic response as a linear function of the initial disturbance and external load, which is of great help to understand and solve the dynamic problem of linear structural system. Based on dynamic explicit formulation, this dissertation studies the fast algorithms for non-stationary random response analysis of heterogeneous material structures and active control of large-scale linear structures. The main research contents are as follows:Firstly, an efficient multiscale strategy for non-stationary random response analysis of heterogeneous material structures is presented. It can be concluded that, from the fundamental theorys of pseudo-excitation method and time-domain explicit method, the key to fast solve the problem is to improve the computation efficiency of a single dynamic analysis of heterogeneous material structures. Thus, a dynamic extended multiscale finite element method is developed. Based on the equivalent static equilibrium equations at each time step of dynamic analysis, the multiscale basis function is established by using numerical method, which can both reflect the microscopic heterogeneity and dynamic properties of heterogeneous materials. Then, the problem can be solved at macroscale, meanwhile, the micro solution at arbitrary location can be acquired conveniently by downscaling calculation. Compared with traditional finite element method, the computation efficiency is dramatically increased. Furthermore, by combining the dynamic multiscale finite element method with pseudo-excitation method and time-domain explicit method respectively, a unified multiscale framework is proposed, which can be used to realize the fast calculation for non-stationary random response analysis of heterogeneous material structures.Secondly, a series of novel fast model predictive control algorithms for large-scale linear structural dynamic system are presented. For linear time-invariant structural dynamic system, the dynamic explicit formulation is introduced into standard model predictive control algorithm to compute the system state of each prediction point in a prediction period, which can prevent matrix exponential operation, therefore, the computation efficiency is greatly improved. Furthermore, by applying the physical meaning of dynamic explicit formulation to compute the optimal control force, a great number of matrix-matrix multiplications are avoided, which greatly reduces the computation memory, improves the off-line computation efficiency and ensures the on-line computation efficiency. For linear time-invariant structural dynamic system with input-delay, on the basis of fast algorithm of no-delay system and by introducing an augmented state vector, the input-delay differential equation is transformed into the standard form without any explicit time delay, so as to realize the fast model predictive control for linear time-invariant structural dynamic system with input-delay. Because no approximation and assumption are involved in the whole process, the system performance and stability are easily guaranteed. In addition, by introducing the time-variant dynamic explicit formulation into standard model predictive control algorithm, the fast model predictive control for linear time-variant structural dynamic system is realized with no computation of time-variant matrix exponential and the computation efficiency is greatly improved.Finally, based on the SiPESC software platform, a new general algorithm framework for linear structural time integration analysis is constructed by using plug-in technology and software design mode, in which the algorithm and data are separated. Using this framework, a series of classical algorithms are implemented, including Newmark method, Wilson-θ method, and HHT method etc.