Study Of Orthogonal Experiments Based On Object-oriented Finite Element Programming And Its Application In Structure Optimization

Structure optimization is a comprehensive subject composed of mechanics, mathematical programming, computer science and other engineering subjects. It has been one of the most important tools of modern structure optimization. Currently, the application fields of structure optimization contain not only aviation, but also ship, bridge, automobile, mechanic, architecture and so on. The types of problems solved by structure optimization have extended from reducing the weight of structures to decreasing the levels of stress, improving the performance of structures and increasing the safe life. Orthogonal experiments have the properties of uniform distribution and regularity, and comprehensive information can be obtained by a few experimental points. Orthogonal experiments can optimize from multi-directions without derivation. Therefore, it is important to apply orthogonal experiments to structure optimization.Object-oriented finite element programming and orthogonal experiments have been researched widely. This paper constructs large-scale orthogonal tables independently and improves the algorithm of orthogonal experiments in order to realize the application in structure optimization. The bottom structure of finite element analysis and optimization has been developed by the platform of .NET. The main work of this paper can be stated as follows:(1) Based on the high expansibility, low coupling, polymorphism and inheritance of the objected-oriented programming idea, the object-oriented finite element programming idea is introduced to develop the bottom structure of finite element analysis and optimization in this paper. The bottom structure offers the necessary data and functions for the following orthogonal experiments. After analyzing the common characteristics among the finite element models, objects are recognized according to different functions and these objects compose a class library for finite element analysis and optimization. The class library contains individual classes and management classes, which are use to define the element attributes and do some finite element analysis (statics analysis or modal analysis) respectively. It can also commission the mathematics class to compute and the optimization class to optimize. With the characteristic of inheritance, it can easily analyze any types of elements. Moreover, there are some class diagrams described the inheritance, polymerization and commission by UML.(2) There are few orthogonal experiments in traditional commercial software, as a result of the difficulty of constructing large-scale orthogonal tables. According to the definitions of finite field, whole vectors and independent vectors, normal orthogonal tables for complex structure are developed in this paper. A general orthogonal table can only solve the problems with no more than 20 factors under 2 to 5 levels. However, the orthogonal tables proposed in this paper can solve the problems with 1500 factors under 2 to 10 levels at least, so there will be no problems about constructing large-scale orthogonal tables. Furthermore, because there are only numerical simulations in this paper, the experiments will not increase more experimental cost.(3) If only one orthogonal experiment is implemented at a time, maybe no feasible solutions will be found. So an adaptive orthogonal experiment is presented in this paper. The convergence factor and iteration times are determined before the experiments begin. Through analyzing and contrasting with the results of every experiment, one can obtain the better experiment of this iteration and modify the levels of the factors according to this better experiment and convergence factor. Then a new iteration begins and one can follow the steps above. The experiment field is convergent and the solutions are getting closer to the optimal solution gradually. So the solutions of orthogonal experiments can fall into the feasible field finally.(4) The amount of experiments in orthogonal experiments is proportional to the factors. There are much more factors in large-scale structures and if the factors are all considered, it will not only increase more ineffective experiments, but also offend the constraint conditions undoubtedly. So one can do the sensitivity analysis first and then do the orthogonal experiments. The sensitivity analysis can choose the most influential parameters and make these parameters as factors, so it is effective to reduce the factors and the amount of experiments.In order to prove the feasibility and validity of the method proposed in this paper, three truss structures and a frame structure of conceptual car body are adopted as examples in this paper. Through optimizing the cross-sectional parameters in the examples and contrasting the results with these references, some conclusions can be obtained: On the premise of satisfying the constraint conditions, though the solutions solved by evolutionary algorithms are more optimal, the running time of orthogonal experiments is much less. Furthermore, the combination of sensitivity analysis and orthogonal experiments are useful to reduce the computational complexity for large-scale structures. So the method proposed in this paper is feasibility and validity. Finally, there are some conclusions about this paper and the working directions about the future.