基于减基法的结构快速设计方法及其应用

发布时间：2018-02-20 08:18

本文关键词： 减基法结构设计快速设计有限元法　出处：《湖南大学》2012年硕士论文　论文类型：学位论文

【摘要】：数值模拟技术是现代产品设计方法的重要组成部分，其提高设计质量、减少周期的优势明显，已经成为人们定量研究复杂工程对象的必要手段。然而若实际工程结构的有限元模型规模较大时，单次计算将耗费大量时间。在对结构进行优化设计时，此类问题会更加突出，因此，在保证必要求解精度的前提下，提高计算速度对结构设计具有重要意义。为了解决这一问题，国内外学者提出了多种快速计算方法，取得了诸多成果，减基法与有限元法相结合的混合算法属于其中一种。目前该算法仍停留在理论层面，与解决实际工程问题仍有一定距离。本文首先对静力学及模态动力学减基混合算法进行研究，并将其应用到结构的设计中。然后以某矿用车车架为例，将静力学减基混合算法应用到大规模结构快速计算问题中，主要工作如下： 1.针对结构优化计算效率较低的问题，采用一种快速设计方法提高其单次计算效率，该方法将减基法与静力学和模态动力学结合，，形成减基混合算法。在保证计算精度的前提下，计算结构的多种典型工况。该混合算法通过构建特定工况下的解空间将原大规模计算问题转变为小规模问题，而后在典型工况对应的小规模问题基础上，利用优化算法对结构进行优化设计。以空间梁单元车架为研究对象，计算结构在典型工况下的响应。结果表明基于减基混合算法的空间梁单元结构可以得到合理的优化结果，并且整个优化过程节约了大量时间。 2.将该减基混合算法应用到混合壳结构有限元模型，提出了基于参数敏感性分析的减基混合算法，以验证减基混合算法在结构设计中的应用潜力。将减基混合算法同设计参数敏感性分析结合，实现设计参数部分显式化，以解决减基混合算法处理后得到的无参矩阵过多所造成的内存不足的问题，提高计算效率。基于敏感性分析的减基混合算法实现了在大规模问题上的应用，既保证了计算精度，同时又缩短单次计算耗时。研究表明，本方法能得到精度较好的计算结果，并且缩短了单次计算消耗的时间，同时节约了内存空间，提高了计算效率。减基法与有限元法相结合的减基混合算法适用于结构的优化设计中。可以利用该算法快速计算多种典型工况以提高优化计算效率。将减基混合算法应用到大规模结构计算问题中时，利用敏感性分析控制结构分离出的无参矩阵的个数。此法可以提高内存利用率和计算效率。本文的研究结果验证了减基混合算法在结构设计中的应用潜力。
[Abstract]:Numerical simulation technology is an important part of modern product design method. It has the advantages of improving design quality and reducing cycle. It has become a necessary means for people to quantitatively study complex engineering objects. However, if the finite element model of actual engineering structure is large, the single calculation will take a lot of time. When the structure is optimized, this kind of problem will become more prominent. Therefore, on the premise of ensuring the accuracy of the solution, it is of great significance to improve the calculation speed for the structural design. In order to solve this problem, many rapid calculation methods have been proposed by domestic and foreign scholars, and many achievements have been obtained. The hybrid algorithm, which combines subtraction method and finite element method, is one of them. There is still a certain distance from solving the practical engineering problems. In this paper, the hybrid algorithms of static and modal dynamics are studied firstly, and applied to the design of structure. Then, taking the frame of a mine vehicle as an example, The static base reduction hybrid algorithm is applied to the fast computation of large scale structures. The main work is as follows:. 1. Aiming at the low efficiency of structural optimization calculation, a fast design method is adopted to improve the efficiency of single calculation. The method combines base reduction method with statics and modal dynamics. Under the premise of ensuring the accuracy of the calculation, the hybrid algorithm is used to calculate the typical conditions of the structure. The hybrid algorithm transforms the original large-scale computing problem into a small scale problem by constructing the solution space under specific conditions. Then on the basis of the small scale problem corresponding to the typical working conditions, the optimization algorithm is used to optimize the design of the structure. The space beam unit frame is taken as the research object. The results show that the spatial beam element structure based on the modified hybrid algorithm can get reasonable optimization results and the whole optimization process saves a lot of time. 2. The hybrid algorithm is applied to the finite element model of the hybrid shell structure, and a hybrid algorithm based on parameter sensitivity analysis is proposed. In order to verify the potential of the hybrid algorithm in structural design, the hybrid algorithm is combined with the sensitivity analysis of design parameters to realize partial explicit design parameters. In order to solve the problem of lack of memory caused by the excess of nonparametric matrix, the algorithm based on sensitivity analysis is applied to large scale problems, and the accuracy of calculation is guaranteed. At the same time, the time of single calculation is shortened. The results show that this method can get good calculation results, shorten the time consumed by single calculation, save memory space and improve the efficiency of calculation. The hybrid algorithm of base reduction combined with finite element method is suitable for the optimization design of structure. It can be used to calculate several typical working conditions quickly to improve the efficiency of optimization calculation. In the model structure calculation problem, By using sensitivity analysis to control the number of nonparametric matrices separated from the structure, this method can improve the memory utilization and computational efficiency. The research results in this paper verify the potential application of the base reduction hybrid algorithm in structural design.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O242.1;TH122

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