Topology Optimization Design Of Functionally Graded Materials Based On Modified Variable Density Method

Topology optimization technology solves the engineering problem of how to find the most reasonable material distribution within the prescribed design domain effectively, which happens in the conceptual design phase. After nearly three decades of growth, topology optimization has been extensively applied to various fields, covering the macro structural design to the microscopic material design. Topology optimization design of the micro material can give rein to the potential of material performance, thus, materials with unique special properties can be designed. In order to accommodate the gradient of the external environment,the item of functionally graded materials has been put forward, it is characterized by the physical property varies along a certain direction. This paper addressed the topology optimization design of functionally graded materials research, the main work is as follows:Firstly, this paper put forward an improved variable density method, which based on the moving limit self-adaptive mechanism, significantly accelerated the convergence of topology optimization problem. As one of the critical parameters which impact on the iteration step length directly, moving limit can strongly affected the structural convergence rate. The writer corrected it from the constant variable to a self-adaptive variable, which makes an adjustment based on the change in the design variables. This modified method can enhance optimize efficiency without destroying the optimal topology. Two classic examples in the field of topology optimization are employed to verify its feasibility and fast convergence.Secondly, this article studied the topology optimization of continuum microstructure,which arranged by an array of periodically unit cells, proposed the design methodology based on the modified variable density method to optimization the unit cell. Four numerical examples of the microstructure design are applied to prove the effectiveness of the proposed method to optimization material microstructure.Thirdly, this thesis researched the topology optimization of functionally graded materials with extreme physical performance, adopted the nonlinear diffusion method to ensure the connectivity of material structures, and established its general design flow using the improved variable density method. Through several numerical examples, functionally graded materials which satisfy the Hashin-Shtrikman-Walpole upper bounds of bulk/shear modulus are obtained, thus demonstrates this modified method can design such FGMs with extreme physical performance effectively.Finally, this paper studied the topology optimization of functionally graded materials with specific properties, minimized the energy functional of the material density gradient to guarantee the continuity of the overall microstructure, and built its general design flow basedon the modified variable density method. Considering the physical properties of negative Poisson's ratios, functionally graded materials with the specified Poisson's ratios are obtained through two analysis examples, which show the validity of this improved method to optimization such FGMs with specific properties.