【作者】 孙蓓；

【导师】 苏超；

【作者基本信息】 河海大学 ， 水工结构工程， 2005， 硕士

【摘要】 结构拓扑优化是近年来国际结构优化研究领域最热点的问题之一,它使复杂结构在概念设计阶段即可灵活理性地进行方案优选。随着其理论发展的日趋成熟,将其从单纯理论研究发展到工程实践应用阶段的条件也日趋成熟。本文在阅读大量外文文献的基础上,深入研究了拓扑优化的基本理论,就其在水工结构优化设计领域的应用进行了初步探讨,主要研究工作有:1. 使用结构拓扑优化方法中发展最成熟的方法-均匀化方法,探索性地研究了利用结构拓扑优化技术进行水工结构优化设计的具体方法。以微结构单胞为基础,解释了均匀化方法的数学模型和求解算式。2. 以有限元为工具,根据水工建筑物结构设计的具体情况,借助于体积分量设计变量的空间分布来描述可选择的结构设计,将固体普通双材料混合小应变算法改进发展成为Voigt-Reuss简化模型,使计算量显著缩减。利用ANSYS软件的APDL语言自行开发了拓扑优化程序,从技术角度实现了水工建筑物的结构拓扑优化。3. 从偏微分方程反问题的角度解释了结构拓扑优化中棋盘格式、网格依赖性等数值不稳定现象的本质。结合数字信号处理中的高斯函数滤波法和流体力学中的多重网格法,提出了一种新的综合解决方案,同时引入了滤波半径延拓法减少局部极值现象对结构优化全局的影响。4. 在减少了连续体结构拓扑优化方法的求解规模并成功解决数值不稳定现象后,将该方法引入到混凝土重力坝的拓扑优化设计中,比较了拓扑优化方法和传统优化方法的优化结果,计算结果表明连续体结构拓扑优化方法完全胜任于水利工程的优化设计,应用前景较为广阔更多还原

【Abstract】 Recently, topology optimization is the hottest problems in international structure optimization filed, through which better schemes can be chosen in concept design stage. Development becoming ripe with its theory, grow from pure theoretical research to project practice terms of the application stage ripe becoming appropriate. This text study the topological basic theories and discuss the application in the field of hydraulic engineering on the basis of reading a large number of foreign reports, the most works are:1. This thesis investigates the design problems of hydraulic engineering using homogenization method, which is the most mature method in topology optimization. It explains the mathematics homogenization method model and formulaon the base of microstructures.2. Alternative hydraulic engineering structural design are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain, Small-strain integration algorithms for general two-material mixtures of solids are developed for the Voigt-Reuss assumption, and the number of calculations is cut short. This text empoldered topology optimization program using APDL language of ANSYS, and it realized topology optimization of hydraulic engineering form the point of the view of technique.3. Form the point view of inverse PDE, the essence of numerical instabilities in the topology optimization is given, including checkerboard pattern and mesh-dependence. Based on this explanation, a novel method-Gaussian method and multi-grid method are proposed, then extended radius of filter wave are introduced to reduce the influence of local extremum phenomena.4. After decreasing the computation scale and solving the numerical instabilities, we use the continuum topology optimization to design hydraulic engineering, and compared the results in topology optimization with the results in traditional optimization, the outcome showed that topology optimization is better and the it is widely use.更多还原