Sensitivity Analysis And Design Optimization For Thermal Coupled Structural System

The design of thermal coupled structural system is a very common research problem in many industrial engineering such as astronautics, aerospace, engine and chemical machinery. The analysis and design of the system, which includes heat conduction, structural response (displacement, stress, buckling, vibration) and the coupled interaction of the two disciplinary, is the essential task for the engineers. On the other hand, the design optimization of heat conduction for engineering structures has wide range applications in practice. Therefore the research of design optimization of thermal coupled structural system will be of great significance in the respect of theory and engineering. This research belongs to one of the categories of Multidisciplinary Design Optimization (MDO) and then its achievements will place a good foundation of the theory and the software for future work which takes more kinds of disciplinary into account.The research in the dissertation consists of two major parts. The first part includes the analysis and sensitivity analysis of steady state and transient heat conduction, the construction of design model and the algorithms of design optimization for heat conduction. The second part involves the coupled design optimization of thermal structures, which takes the thermal displacement, thermal stress, thermal buckling and thermal vibration into account, hi this part, the main contents are the theory and computational schemes of sensitivity analysis, the techniques of software design and the algorithms of design optimization for the coupled system. The research work will be introduced with the following chapters.In chapter 1, the research developments of MDO in the recent 20 years are surveyed, which include the solution algorithms of the design optimization model for MDO, the applications in engineering, the design of software system, the research organizations and academic activities. In the following section, the research of design optimization of thermal coupled structural system is reviewed. Three contents, which are the analysis of thermal structures, the analysis and design optimization of heat conduction, the design optimization of thermal structures, are summarized in this section. And then, the finite element software system of structural analysis and design optimization, which is the platform of this work, is introduced. In the last section, the brief description of the research in this dissertation is presented.In chapter 2, the precise time integration (PTI) method for the analysis of transientsystem is discussed. As for linear problem, the detail procedures of the algorithm and several integral formulations for different kinds of non-homogenous terms are presented. As for nonlinear problem, the approximation schemes and the error analysis of PTI are investigated, In order to avoid the computation of inverse matrix, the PTI with dimensional expanding is proposed. The methods of constant, linear, sinusoidal approximation are proposed for the transformation of non-homogenous terms. The computational expense of the new method is also discussed.In chapter 3, the heat conduction analysis is investigated. Firstly, the conventional methods of steady state and transient problems are reviewed. And then the PTI method is applied to the solution of transient heat conduction. The general formulation of PTI, the substructure method of PTI, and the proof of symmetry property of matrix exponential in PTI are proposed. As for the nonlinear problem, the predictor-corrector algorithm, which possess 2nd precision of numerical results, is presented. The application of adaptive PTI method is also given. Finally, the 4-nodes finite element for heat conduction of shell structures is presented.In chapter 4, the sensitivity analysis and design optimization of heat conduction is investigated. The sensitivity equations are deduced based on the discrete model by the direct method and adjoint method respectively. The conventional solutions methods are given. In the next section, the semi-ana...