Investigation On The Key Theory And Methods Of Topology Optimization Of Materials And Structures

Topology optimization has been rapidly developing in the last two decades and is now extended in new application areas at an increasing rate, because it achieves by far greater savings and design improvement than sizing or shape optimization. Its intrinsic capacity of simultaneous optimal design of materials and structures promises to attain higher material and structural efficiency in aerospace and automobile industries, where some indexes such as weight are crucial to the performance of structures. In general, structure optimization and material design are dealt with based on the same topology optimal techniques in different scales. Currently, the potential ability of topology optimization is not fully explored, as material layout and design of microstructure are separated in the design procedure. It is necessary to investigate the integrated design methodology of materials and structures for designing the multifunctional material and structural system and removing the frontier etween materials and structures. The main research work in the dissertation will be introduced as follows:A generalized perimeter scheme with weak rotational mesh-dependence is proposed to prevent numerical instabilities associated with checkerboards and intermediate densities in topology optimization. The scheme of quadratic form means that it is easy to establish a suitable explicit approximation and favors its implementation in convex programming. Based on the characteristics of density design variables associated with multiphase materials, the general concept of perimeter is extended and four kinds of perimeter control methods are proposed for topology optimization multiphase materials. Several 2D and 3D optimal examples made of two or three different materials phases are carried out for the compliance minimization. It shows that checkerboards and intermediate values of density variables are able to be eliminated efficiently.Using the homogenization method and the finite element method, the effective properties and the sensitivities with respect to element densities of material microstructures are calculted. A multi-objective model is presented to optimize the topology of the microstructure with two or three-phase materials, subject to constraints on volume fraction and perimeter control. A comparative study is carried out for design of microstructures with the extreme properties and the prescribed elastic properties including the modeling and the algorithm. Several designs of microstructures with the prescribed properties are tested. These works are the basis for the integrated design of materials and structures.Inspired by hierarchical structure of natural or biological materials, an computational model for the integrated design of materials and structures consisting of hierarchical cellular material levels or layers is described and an integrated design methodology is proposed for the global stiffness maximization of the overall structure and local design of material microstructures based on the homogenization method of multi-scale computing. The optimal design procedure includes two steps. Firstly, the material layout is figured out. Secondly, topologies of microstructures of intermediate density materials are designed. Numerical results show that the proposed method is well adapted to the design of lightweight structures. In addition to this, another issue about influences of microstructure aspect ratio on the optimal design is discussed and numerical experiences show that the integrated design methodology based on homogenization method is unable to reflect scale effect. The three-phase material integrated design is investigated and computational results illustrate the procedure.An integrated design methodology characterizing Representative Volume Element scale is proposed. Based on the proposed concept of design element (DE), designs of materials and structures are dealt with in a unified way. By changing the periodic arrangement, the scale and aspect ratio of the DE, scale-related effects are well revealed and distinguished in the final optimal results. Furthermore, numerical design problems for 2D layered structures with cellular core, three-phase material structures, circular structures and cylindrical grid structures are investigated to illustrate the proposed approach.Topology optimization of weakly coupled thermo-elastic problems in steady state is discussed. The optimal design is decomposed into three sub-problems. Numerical results are obtained in different thermal loading cases. Different interpolation schemes are compared for maximizing the thermal conduction efficiency. It is shown that the optimal model affects optimal design subject to distributed heating over the structure. To study the scale-effect, the multi-objective design associated with rigidity and thermal conduction is performed by considering the whole design domain and the periodic partitionof the design domain. Finally, truss structures with uniform temperature distribution are analyzed and optimized. Different penalty approaches are tested to prevent intermediate densities and influences of penalty parameter on optimal results.