Space Truss Topology Optimization Design Under Buckling Constraints

Truss topology optimization problem under local stress constraints and local buckling constraints is one of the most challenging research topics in the field of structural topology optimization on both of the theoretical and application aspects. The resolution of this kind of problem is very important for the successful application of topology optimization method to the real-life engineering design. To deal with the so-called jumping of the buckling length phenomenon, a new formulation and the corresponding algorithm for the solution of truss topology optimization problems under buckling constraints has been proposed by Cheng GengDong, Guo Xu and Olhoff recently. By employing this new formulation, the numerical difficulties arising from singular optimum and jumping of the buckling length can be solved in an elegant way. In the previous work, only planar trusses and small-scale problems are considered. In the present thesis, we have generalized above research work to space trusses and developed the corresponding algorithms for the solution of mid-large scale problems. The thesis is organized as follows:In the first chapter, we give a brief review of the current research activities of structural topology optimization. In the second chapter, the so-called singular optimum phenomenon is discussed and difficulties associated with singular optima are pointed out. We also give an explanation of the importance of the research of singular phenomenon. In chapter 3, we discuss the problem formulation of the truss topology design under local buckling and stress constraints. We also derive the geometry stiffness matrix of truss element and the sensitivities of objective function and constraint functions with respect to design variables. Numerical optimization algorithm for mid-large scale optimization problems is developed and the strategies for the improvement of numerical performance of the optimization algorithm are also discussed in chapter 4. We also discussed the possibility of including the cost of joints in the objective function. It is shown from numerical examples that the number of overlapping bars in the final optimal topology can be reduced to some extent by employing this approach, which is meaningful for real-life engineering structural design. Many numerical examples are presented in this chapter for the demonstration of the effectiveness of our optimization algorithm. Finally some concluding remarks are given. Some possible further research opportunities are discussed.