Structural Stiffness And Seepage Multifunctional Material Design Based On Topology Optimization

Engineers are always seeking for structural design with better performance. Structural op-timization provides them a powerful approach to find the optimal design of engineering prob-lem. In comparison with sizing and shape optimization, topology optimization is being used extensively to obtain a creative structural configuration at the conceptual design stage.Fluid transfer in porous media is a very universal phenomenon and has a strong background of applications such as filter and transpiration-cooled thrust chamber which are made of porous media. It is needed to develop an optimization method to design a high effective structural con-figuration considering the performances of seepage and stiffness simultaneously. Focusing on the material/structure multifunctional and multiscale optimization problem, we have improved and proposed some effective algorithms from multiple angles aiming at improving the efficiency and convergence of algorithms in structural topology optimization and material microstructure design.SIMP (Solid Isotropic Material with Penalization) model is currently the most widely used in many kinds of topology optimization problems because it is very easy to be implemented and fits for many kinds of optimization problems. Another very important advantage is that it can be linked with the general finite element packages very easily. Density filter is a very effective regularization scheme to deal with the numerical difficulty such as checkerboard and mesh dependency in topology optimization. However, when density filter is used, some grey el-ements often emerge along the material boundary which cause difficulty in extracting structural boundary from the optimal topology result. Heaviside nonlinear density filter can eliminate grey domain along material boundary, but it can not maintain the material volume which causes oscillation during optimization iteration. A new volume preserving nonlinear density filter has been proposed which can guaranty material volume preserving before and after nonlinear trans-formation of density field. With the volume preserving nonlinear density filter, the iterative process of optimization is very stable and the optimization efficiency is improved.For 3D (three dimensional) structural topology optimization with element or node density as the design variable, the optimization problem is very large in size and difficult to solve. AMR (Adaptive Mesh Refinement) finite element method reduces the number of displacement variables in finite element model remarkably and increases the accuracy and efficiency of finite element analysis. Following the idea of AMR finite element method, a AMR based topology optimization method was proposed to optimize the field of design variable for decreasing the amount of design variables in topology optimization. At the initial stage of optimization, the tendency of material distribution can be obtained with a very coarse mesh efficiently. Then, the mesh is remeshed with AMR rule based on the information of density field of topology optimization. The amount of mesh around material boundary is increased and that of mesh far away from material boundary is decreased. In comparison with the traditional topology optimization, AMR based topology optimization can obtain the optimal material distribution which having smooth material boundary with fewer design variables and higher efficiency.Material design is an important application field for topology optimization. The optimal result is influenced by both the type of initial density distribution and the value of optimiza-tion control parameters when designing material microstructure with inverse homogenization method. The type of initial density distribution which often depends on the experience of de-signer is very difficult to be determined. Crystallon is usually used to accelerate crystal's growth when making cultured crystal. Inspired from this physical process, a new method called Crys-tal Nucleus Method (CNM) was proposed to determine the initial density distribution. Some issues about this method were studied which including the position of crystal nucleus, the value of power exponent in SIMP model, the density filter domain and the type of object function. Optimal material microstructures with described and extreme performances were successfully obtained with this method.The microstructure of material is designed to optimize the multifunctional performances of stiffness and seepage of macrostructure which is made of porous media with periodic mi-crostructure. Generally speaking, there is no simple relationship between stiffness and seepage performances of structure made of material with periodic microstructure. The performances of stiffness and seepage are determined by the effective elastic property and permeability coeffi-cient which are both related to the microstructure of material. The microstructure of material and the stiffness and seepage performances of macro structure are connected through the ef-fective elastic tensor and permeability tensor of material. To design optimal microstructure for the stiffness and seepage performances of macrostructure is a multifunctional and multi-scale optimization problem. It is a challenging research topic in theory and application. For the present study, the macrostructure made of macro homogeneous material with periodic mi-crostructure is considered as linear elastic structure and the macro flow of fluid is governed by Darcy equation. Driven by the stiffness and seepage performances of macrostructure, the opti-mal mi crostructure was obtained with the method of inverse homogenization. Adjoint method was used to calculate the sensitivity of flow rate and effective permeability coefficient with re-spect to the element density. Based on the Darcy-Stokes model, optimal material microstructure for maximization of effective permeability under the given amount of solid material is obtained with reasonable precision by designing fluid channel in the domain of material cell by CNM and AMR based topology optimization. For multifunctional material design considering structural stiffness and seepage performance, two optimization models were proposed which were multi-objective design of structural stiffness and seepage performances and structural stiffness design under specified seepage flow rate. Optimal microstructures of 3D material were obtained with different design parameters. For the optimization of maximizing structural stiffness under the prescribed flow rate, the volume preserving nonlinear density filter can make the optimization process more stable.