Two-scale Topology Optimization Of Continuum Structures Under Buckling Constraints

As the rapid development of computer technology and refinement of structural optimization theory, the structural topology optimization techniques have been widely used in more and more fields, and become an important tool for improving the quality of structural designs. Due to the variety and complexity of practical engineering problems and increasing demands for solving larger scale optimization problems, there are still many new challenges in research on the theories and algorithms of topology optimization. For example, structural stability is an important factor for assessing a structural design, yet there are still some major difficulties when the buckling constraint is considered in topology optimization of continuum structure. On the other hand, while it is now an effective method to achieve the lightweight of structure and improvement of design quality by simultaneously optimizing the structure and material, the multi-scale optimization models and algorithms are still in the development stage and more research effort is required. This dissertation makes an investigation on the multi-scale topology optimization of continuum structures under buckling constraints, and the main contents are as follows.1. The pseudo eigenmodes are investigated and a general method is developed to deal with such this problem in linear buckling and natural frequency optimization. In order to deal with the pseudo modes that may appear in the low-density region in the eigenvalue optimization, the characteristics of these pseudo modes are investigated firstly, and then a method based on combining use of the eigenvalue shift and pseudo modes identification is proposed.2. The topology optimization of continuum structure for minimum structural compliance under volume and buckling constraints are studied, and two-phase algorithms and a modified continuation penalization method are developed to overcome the disadvantages of existing algorithms. It is discovered that the optimized results obtained using the conventional algorithm may not be as good as expected, and thus the two-phase algorithms and the modified continuation penalization method are proposed. The numerical examples presented show that the quality of optimized design can be improved significantly by using the proposed methods.3. To confirm the effectiveness of proposed method for dealing with pseudo eigenmodes in dynamic optimization, the topology optimization problem for maximum structural fundamental frequency under volume constraint is studied. The numerical tests conducted demonstrate the versatility and reliability of the proposed method. Moreover, different algorithms are employed in the tests, and their performance is compared and discussed.4. The two-scale topology optimization problem for minimizing structural compliance under volume constraint is considered, and a modified concurrent topology optimization model with the orientation of material microstructure as a new design variable is proposed. After the disadvantages of existing two-scale optimization models are discussed, the new model is developed. The three types of independent design variables in this model represent the relative densities of elements at both macro and micro scales and the orientation of material microstructure, respectively. The homogenization method is applied to integrate the two-scale optimization into one system, and an automatic distribution of base material between the two scales is achieved through the optimization. To further improve the design quality by avoiding local solutions, an orientation adjustment strategy is also developed. The numerical examples show that the quality of the optimized design is greatly improved by using the proposed model and algorithm.5. The two-scale topology optimization problem for minimizing structural compliance under volume and buckling constraints is studied, and an effective algorithm is developed based on the new techniques presented above. Different optimization models are considered in the numerical tests, and solutions of several optimization problems are presented and compared. This study has shown that the performance of structures with porous material can be significantly improved by employing the new two-scale optimization model.