刚度扩散法及其应用研究

发布时间：2018-04-08 12:01

本文选题：刚度扩散法　切入点：协同优化　出处：《华南理工大学》2013年硕士论文

【摘要】：刚度扩散法是适用于多组件系统优化设计的一种新方法。该方法最初是针对桁架结构布局优化而提出的，其新颖之处是在桁架优化问题中引入了背景网格，从而使桁架杆件可以在设计域内自由移动，因此优化问题设计空间不会像在采用传统的基结构方法时那样被限制。刚度扩散法通过特定的插值方法，将离散组件的刚度矩阵进行转换，从而使组件节点与背景网格节点不重合时有限元分析仍然可以进行，而且在转换后结构响应量相对设计变量的敏度可以用解析的方法求出。本文首先对刚度扩散法中响应量的插值方法进行了研究，对其中关键参数紧支半径的影响进行了考查，并给出了其建议的取值范围。在此基础上，本文提出了一种基于修正Shepard插值模型的新插值方法，并将这种新的插值方法应用到了桁架结构布局优化以及桁架杆件与连续体结构的协同优化中，同时对刚度扩散对杆件刚度的影响进行了研究，数值算例的结果说明新的插值方法是一种高效而稳定的方法。其次，本文研究了导热系统的优化问题，提出了热管的简化模型，并构造了由热管和连续体所构成的散热系统的协同优化模型。在该导热协同化模型中包括表示散热系统中热管的位置以及表示连续体的拓扑的两类设计变量，实现了导热系统中热管位置及连续体拓扑的同时优化。本文还对协同优化问题中不同种类设计变量间的相互影响进行了研究，提出了适用的优化策略。最后，对全文工作进行了总结，并对未来的研究工作提出了建议。
[Abstract]:Stiffness diffusion method is a new method for optimal design of multi-component systems.This method was originally proposed to optimize the layout of truss structures. The novelty of the method is that the background mesh is introduced into the truss optimization problem, so that the truss members can move freely in the design domain.Therefore, the design space of the optimization problem is not limited as the traditional basic structure method.The stiffness diffusion method transforms the stiffness matrix of discrete components through a special interpolation method, so that the finite element analysis can still be carried out when the node of the component does not coincide with the background grid node.Moreover, the sensitivity of the structure response to the design variable can be calculated by analytical method.In this paper, the interpolation method of the response quantity in the stiffness diffusion method is studied, and the influence of the key parameter on the radius of the compact support is investigated, and the range of the suggested values is given.On this basis, a new interpolation method based on modified Shepard interpolation model is proposed and applied to the layout optimization of truss structure and the cooperative optimization of truss member and continuum structure.At the same time, the effect of stiffness diffusion on the stiffness of members is studied. The numerical results show that the new interpolation method is an efficient and stable method.Secondly, the optimization problem of heat conduction system is studied, and the simplified model of heat pipe is proposed, and the cooperative optimization model of heat dissipation system composed of heat pipe and continuum is constructed.In the model, two kinds of design variables are included to represent the position of heat pipe and the topology of continuum in the heat transfer system. The optimization of the position of heat pipe and the topology of continuum in the heat conduction system is realized.In this paper, the interaction between different design variables in cooperative optimization problem is studied, and the suitable optimization strategy is proposed.Finally, the paper summarizes the work and puts forward some suggestions for future research.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU311.4

【参考文献】