基于改进的灵敏度分析的有限元优化技术研究

RESEARCH OF THE OPTIMAL DESIGN BASED ON THE FEA AND IMPROVED SENSITIVITY ANALYSIS

随着计算机科学和有限元技术的发展,各种通用有限元分析程序在给定结构模型的性能计算方面已趋成熟。但是基于有限元的优化设计技术还存在很多缺陷,其中一个重要原因在于设计灵敏度分析技术尚需不断改进。将灵敏度分析研究的最新成果及时应用于通用有限元程序,不但能大大减小计算方面的编程量,使得研究者把精力主要放在关键的灵敏度分析技术上,更有效地解决工程问题;另一方面,也可以籍此为灵敏度分析提出新的研究方向。文中在计算效率高、实现容易的半解析灵敏度分析方法的基础上,通过引入刚体运动空间对虚载荷进行修正,从而达到对半解析灵敏度分析方法进行改进的目的,在很大程度上消除了半解析法采用有限差分近似计算虚载荷时固有的病态误差问题,大大提高了计算精度。结合大型通用有限元程序ANSYS,完成某复合材料机翼结构打样阶段优化设计,减重效果明显,并就计算中发现的问题对灵敏度分析进行展望。重点推导虚载荷的修正公式、讨论改进的灵敏度分析算法在ANSYS中的实现方法和技巧。改进算法不依赖于单元类型,且其实现不依赖于有限元程序源代码,所以文中的研究工作具有一定的通用性。

With the development of computer science and finite element method, many commercial finite element packages can quite well provide the structural behaviors for a given model. But the optimal design technology based on the finite element method is not so mature in the large structures, which is enslaved to the design sensitivity analysis, The difficulties on program code and application can be reduced distinctly by coupling the latest sensitivity analysis technology with an analysis solver such as commercial finite element package, So the research can be focused on the more important aspect of sensitivity analysis, which is useful in the engineering problems. The application in the engineering structures can also promote the development of sensitivity analysis technique. The efficient and easy semi-analytical sensitivity analysis is improved by taking full advantage of analytical differentiation of rigid body modes. The abnormal errors can be reduced distinctly by modifying the load, which mainly contributes to the total errors in the finite difference process. The method is coupled with ANSYS to accomplish the optimal design of one composite wing, and the weight is reduced distinctly. The present article presents the modified formulation of pseudo load of semi-analytical design sensitivity, and the implementation procedure and computational technique in the ANSYS, The modified formulation is independent of the particular element, and the implementation is independent of the ANSYS source code, so the method can also be used into other packages with minor modification.