Study On Vehicle Structural Topology Optimization Design Under Uncertainty

With the increasing pressure of environmental protection and energy saving, the lightweight vehicle design has become the inevitable development trend, and the main technical methods are including: structural design optimization, application of lightweight materials, advanced manufacturing process, etc. Among them, the topology optimization method is considered as the representative of the advanced structure design technology in the automotive lightweight design field.However, in the process of structural design optimization, all kinds of uncertainties factors, such as geometric structure, initial boundary conditions, material properties, loading conditions, and the calculation model, are bound to cause the structural performance fluctuations, and even lead to failure. This means that the structural topology optimization method under deterministic is limited in the vehicle lightweight design. Therefore, the innovation for the theory and method of the automotive topology optimization is necessary. In view of the above requirements, this paper is focused on the application of the continuous structure uncertainty topology optimization method in the vehicle lightweight design:(1) The numerical instability problem in the topology optimization of continuum structures is presented. The filtering method based on the linear diffusion partial differential equation is presented. According to the essential characteristics of numerical instability and the action mechanism of partial differential equations, three kinds of solving methods are established, including explicit finite difference method, semi implicit finite volume method and full implicit finite element method. Based on the anisotropic diffusion partial differential equation, the problem of the grid format, the grid dependence and the gray level units are effectively improved.(2) For reliability problem of the vehicle lightweight design, the pre-reliability analysis of single decoupled scheme for reliability-based topology optimization is provided. The general mathematical model for reliability-based topology optimiztion is estabilished. The pros and cons and applicable ranges of two level approaches, single loop approaches and single decoupled approaches are summarized. The proposed method is applied to the uncertainty problems of the load condition and material properties of the control arm design and the connection of reliability analysis and lightweight design are realized. The calculation accuracy and efficiency are well-behaved, and the proposed scheme consists in finding the best compromise between cost and reliability. The program is relatively simple and easy to implement in commerical software.(3) For robustness problem of the vehicle lightweight design, the sparse grid tehnique based robust topology optimzation is provided. Based on the integral rule, three kinds of sparse grid models are constructed including, Trapezoidal, Clenshaw-Curtis and Causs-Patterson sparse grids. The general mathematical model for robust topology optimiztion is estabilished. The proposed method is applied to the uncertainty problems of loading condition of the control arm design and realizes the accurate estimation of statistical moments, and effectively alleviates the dependence of the number of integral points on the random variable dimensions. Furthermore, to alleviate the “curse of dimension” involved in high dimensional problems. The proposed scheme effectively reduces the performance sensitivity on uncertainties and disturbances, and ensures optimum with optimal performance at the same time, and has excellent computational efficiency and convergence precision. The compromise between robustness and cost is well achieved, and has good engineering applicability.