Continuum Topology Optimization Of The Design

The purposes of structure optimization are economical materials usage and reasonable stress distribution, whereas topology optimization is a important part of structure optimization. A improved structure topology could enhance the structure performance or decrease weight of it, and this lead to more benefit, so topology optimization have been the hot research work in the world in last years. Nowadays topology optimization is explored because of its complicity in models and algorithms. Most work focus on topology theory and method in single loading cases, but fewer efforts have been made in multiple loading cases which are common in real engineering. This thesis studies topology optimization of continuum structures in multiple loading cases based on topology optimization in single loading cases.1. Using Artificial Materials method and SIMP method, suitable design variables and objective function (the minimum compliance) are selected, and a mathematical model, namely the formulation of the minimum compliance problem is set. After that, a effective solving method-principles optimization method is adopted, and the update scheme for the density is deduced. Finally, a series of structure analyses and topology optimization designs are implemented by programming in MATLAB.2. Some problems are analyzed which affect the result of topology designs: (1) checkerboard pattern problem (2) mesh-dependency problem. Filtering the sensitivities technology is found that could solve the problem above successfully. Using this method, a two dimension structure is optimized. Meanwhile, parameters penalty factor and move-limit are discussed. The results show that to change the move limit m, optimized topology would not be affected when using filtering the sensitivities technology, with penalty factor p ≥ 3, and this could supply basis to optimization in multiple loading cases3. Based on the work above, topology optimization in multiple loading cases is studied. The validity of the optimization method presented in this thesis is checked through testing the optimized result in ABAQUS software.