基于动力显式列式的结构振动与控制的快速算法研究

发布时间：2018-07-10 17:29

本文选题：非均质材料结构 + 多尺度方法　；参考：《大连理工大学》2016年博士论文

【摘要】：随着科学技术的不断发展,工程结构日趋复杂化：一方面规模越来越大,例如超高层建筑、大跨度桥梁、大型运载火箭等；另一方面组成越来越复杂,大量新型材料被广泛采用。作为基础设施和公共设施,上述工程结构在运行过程中的安全性和可靠性事关人民生命财产安全,需要格外重视：一方面需要进行动力学分析,以便确定结构在动态载荷下的振动响应；另一方面需要施加必要控制,以便抑制对结构有害的振动。然而,由于上述结构规模庞大、组成复杂,传统方法已难以对其进行高效精确的数值模拟,因此研究适用于复杂结构振动和控制的快速算法具有重要的意义。本文首先从线性结构系统的运动本质出发,结合经典逐步积分法,给出了线性结构系统动力响应的一般表达式——动力显式列式。动力显式列式兼顾了初始扰动以及外载对动力响应的影响,将动力响应显式的表示为初始扰动和外载的线性函数,对于线性结构系统动力问题的理解和求解有很大帮助。以动力显式列式为基础,本文分别就非均质材料结构非平稳随机振动问题和大规模线性结构主动控制问题的快速算法进行了研究。主要研究内容如下：首先,提出了一种适用于非均质材料结构非平稳随机振动分析的多尺度求解策略。从虚拟激励法和时域显式法的基本原理中归纳得出,提高单次非均质材料结构动力分析的计算效率是快速求解非均质材料结构非平稳随机振动问题的关键,据此提出了一种动力扩展多尺度有限元法。该方法以动力分析各时间步内的微观等效静力平衡方程为基础,数值构造出能够同时反映非均质材料微观非均质性和动力特性的多尺度基函数,从而可以在宏观尺度上对非均质材料结构动力问题进行有效模拟,且通过降尺度计算可以方便得到非均质材料结构任意位置的微观结果,在计算效率上较常规有限元法有了很大提高。进一步通过将动力扩展多尺度有限元法分别与虚拟激励法和时域显式法相结合,提出了一种适用于非均质材料结构非平稳随机振动分析的多尺度框架,实现了对非均质材料结构非平稳随机振动问题的快速求解。其次,提出了一类适用于大规模线性结构动力系统的快速模型预测控制算法。针对线性定常结构动力系统,基于标准模型预测控制算法,通过引入动力显式列式来计算预测周期内各预测点系统的状态,避免了矩阵指数的计算,提高了计算效率。进一步通过引入动力显式列式的物理意义来计算最优控制力,避免了大量矩阵乘法运算,极大的降低了计算内存、提高了离线计算效率,并保证了在线计算效率,从而实现了对线性定常结构动力系统的快速模型预测控制。针对具有输入时滞的线性定常结构动力系统,在无时滞线性定常系统快速模型预测控制算法的基础上,通过引入增广状态向量,将时滞差分方程转换为不显含时滞的标准格式,实现了对具有输入时滞的线性定常结构动力系统的快速模型预测控制。整个过程无需近似和假设,系统的稳定性得到保障。针对线性时变结构动力系统,通过在标准模型预测控制算法中引入时变动力显式列式,实现了对线性时变结构动力系统的快速模型预测控制。由于无需计算时变矩阵指数,该方法可以处理较大规模问题。最后,基于SiPESC软件平台,利用插件技术及软件设计模式,研发了一种算法与数据相分离的线性结构瞬态响应通用算法构架,并利用此构架实现了Newmark法、Wilson-θ法.HH T法等经典算法。
[Abstract]:With the continuous development of science and technology, the engineering structure is becoming more and more complex: on one hand, the scale is more and more large, such as super high rise building, large span bridge, large carrier rocket and so on. On the other hand, the composition of a large number of new materials is widely used. As the infrastructure and public facilities, the above engineering structure is in the process of operation. Integrity and reliability are related to the safety of life and property of the people. It needs to be paid extra attention to: on the one hand, dynamic analysis is needed to determine the vibration response of the structure under dynamic loads; on the other hand, necessary control is required to suppress the harmful vibration to the structure. However, the structure is large, complex, and traditional method. It is difficult to carry out efficient and accurate numerical simulation, so it is of great significance to study the fast algorithm suitable for the vibration and control of complex structures. First, the general expression of dynamic response of linear structural systems, dynamic explicit formula, is given from the motion nature of the linear structural system and the classical stepwise integral method. The dynamic explicit formulation takes into account the effect of the initial disturbance and the external load on the dynamic response. The explicit expression of the dynamic response is represented as the linear function of the initial disturbance and the external load. It is very helpful for the understanding and solving of the dynamic problem of linear structural systems. Based on the dynamic explicit column, the nonstationary random material structure is divided into non-stationary random random structures. A fast algorithm for the problem of vibration and active control of large-scale linear structures is studied. The main contents are as follows: first, a multi-scale solution strategy suitable for nonstationary random vibration analysis of heterogeneous material structure is proposed. The calculation efficiency of dynamic analysis of homogeneous material is the key to fast solving the nonstationary random vibration problem of heterogeneous material structure. Based on this, a dynamic expansion multi-scale finite element method is proposed. This method is based on the micro equivalent static equilibrium equation in every time step of dynamic analysis, and the numerical construction can reflect the heterogeneity at the same time. The multi-scale basis function of the micro heterogeneity and dynamic characteristics of the material can be used to simulate the dynamic problem of the heterogeneous material structure effectively on the macroscopic scale, and the microscopic results of any position of the heterogeneous material structure can be easily obtained by the reduction of the scale, and the calculation efficiency is greatly improved than the conventional finite element method. By combining the dynamic expansion multiscale finite element method with the virtual excitation method and the time domain explicit method, a multi scale frame for non-stationary random vibration analysis of heterogeneous material structure is proposed, and the fast solution to the nonstationary random vibration problem of the heterogeneous material structure is realized. Secondly, a kind of application is proposed. The fast model predictive control algorithm for large-scale linear structure power system. Based on the standard model predictive control algorithm, the state of the prediction point system in the prediction cycle is calculated by the standard model predictive control algorithm. The calculation efficiency of the matrix exponent is avoided and the calculation efficiency is improved. The physical meaning of the dynamic explicit formula is used to calculate the optimal control force, avoid a large number of matrix multiplication, greatly reduce the computational memory, improve the efficiency of the off-line calculation, and guarantee the efficiency of the on-line calculation, thus the fast model predictive control of the linear constant structure power system is realized. On the basis of the fast model predictive control algorithm of a time-delay linear constant system, the structural dynamic system, by introducing an augmented state vector, converts the delay difference equation into a standard format without delay, and realizes the fast model predictive control of a linear constant structure dynamic system with input delay. The whole process needs no approximation. The stability of the system is guaranteed. For linear time-varying structural dynamic systems, a fast model predictive control for linear time-varying structure dynamic systems is realized by introducing a time-varying dynamic explicit formula in the standard model predictive control algorithm. The method can deal with large scale problems because of no time variable matrix exponents. Finally, based on the SiPESC software platform and using the plug-in technology and software design pattern, a general algorithm framework for the algorithm and data separation of linear structure transient response is developed, and the classical algorithms such as Newmark method, Wilson- theta.HH T method and so on are implemented.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB53

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