Structural Topology Optimization For Specified Function

Topology optimization is considered as one of the most challenging research fields in structure optimization. During the past two decades, great achievements of topology optimization method have been obtained in both theory studies and engineering applications. Topology optimization methods are usually employed to acquire the best structural performance by designing the distribution of material. In contrast to size optimization method and shape optimization method, topology optimization method can generate more benefits, so it has drawn considerable attention of scholars and engineers. In the early stage of procduct/structure design, topology optimization method has become the main design approach.At the present time, the research scope of topology optimization has extended to structures under the action of multi-physics field. Base on the finite element method, the topology optimization methods of load-bearing structural components, smart structures with piezoelectric actuators and structures for cooling are investigated in this treatise.The dissertation is organized as follows:In chapter 1, reseaches on continuum structural topology optimization are reviewed, which include the history and advance of structural optimization, some major approaches and the range of its application. The progress of study on piezoelectric smart structure and the design of structure for cooling are introduced in general.In chapter 2, under the background of the design of load-bearing structural components of miniature space vehicle, the relationship between the gas consumption rate and the mass moment inertia of the system is deduced as well as the position of mass centre in the state of stable limit-cycle oscillation. It is pointed out that the attitude control efforts increase proportionally with the mass moments of inertia of the system. Topology optimization method of rotational structures considering constraints on the mass moment of inertia is investigated and is applied to design of miniature space vehicles for reducing their attitude control efforts.In chapter 3, the structural analysis method of piezoelectric plannar structure is discussed. Based on this method, the optimal distribution of material under given voltage is studied. The integrated design optimization problem of structural topology and control voltage is further investigated. The flexible structures with piezoelectric patches as actuators are designed. In addition, the applications of this type of structures to the shape variable smart structures are discussed.In chapter 4, the finite element analysis mthod of piezoelectric laminate plates is firstly discussed. Secondly, topology optimization of bimorph-type piezoelectric plates for static shape control applications is investigated. The layout of the piezoelectric layer and the distribution of the actuation voltage are simultaneously optimized, so as to achieve the best overall shape control performance. Penalization on material properties and actuation voltage is peformed to suppress intermediate values of both material densities and control voltage. Further, the integrated optimization problem of piezoelectric material, host layer material and actuation voltage is solved and numerical examples are presented. Finally, Topology optimization method of piezoelectric laminated plates with multilayer piezoelectric material is developed in order to improve the output displacement of piezoelectric smart structures.In chapter 5, the design method described above is applied to design of structure with large aspect ratio. Plannar actuators as well as spatial actuators with repetitive assembling components which have low manufacturing cost are obtained.In chapter 6, topology design of structure for cooling is described. The convergence problem of topology optimization method for structure considering convection boundary conditions is investigated. Topology optimization method of structure under convection design dependent loading is discussed.Finally, the main contributions of the dissertation are concluded and some further aspects of the work are previewed.The supports of Key Project of Chinese National Programs for Fundamental Research and Development (Grant 2010CB832703), Natural Science Foundation of China (90816025, 10721062) and the DFMEC program are gratefully acknowledged.