基于刚度扩散法的多组件系统协同优化设计

发布时间：2019-02-12 17:40

【摘要】：本文基于刚度扩散法提出了若干处理多组件系统协同优化设计的新型优化模型，为多组件系统的协同优化设计提供了新的思路和方法。首先，本文详细介绍了刚度扩散方法的基本原理，主要包括径向基函数插值模型、数学公式推导和灵敏度分析方法，通过若干数值算例说明了径向基函数插值的特点及刚度扩散方法在处理桁架结构布局优化及组合结构优化设计问题时的合理性及有效性。其次，针对杆件与连续体结构的协同优化设计问题，本文首先基于刚度扩散法提出了尺寸固定杆件与连续体结构的协同优化设计模型，通过刚度扩散方法把杆件的刚度扩散到连续体结构的刚度矩阵中，推导了灵敏度分析公式，数值算例验证了所提出模型的有效性。然后在此基础上提出了同时考虑杆件尺寸优化设计的尺寸可变杆件与连续体的协同优化设计模型，同时实现了杆件的布局优化、尺寸优化及连续体结构的拓扑优化。第三，针对弹性体组件与连续体结构的协同优化设计问题，本文首先提出了拓扑固定弹性体组件与连续体结构协同优化设计模型，对弹性体组件划分有限元网格，通过网格节点坐标利用径向基函数插值模型建立弹性体组件位移场与支撑结构位移场之间的联系，通过刚度扩散方法把组件的刚度扩散到支撑结构的刚度阵中。然后在此基础上提出了同时考虑弹性体组件拓扑优化设计的组件与连续体的协同优化设计模型，数值算例表明，本文所提方法同时实现了组件的拓扑优化、布局优化及连续体结构的拓扑优化。第四，通过把支撑视为在特殊位置移动的弹性体组件，利用本文提出的弹性体组件与连续体结构协同优化设计模型，实现了结构支撑位置与拓扑的协同优化设计。另外，考虑到实际工程中施工的难易程度，，在优化模型中加入了支撑的成本约束，得到了不同成本约束下的优化结果，表明成本约束对支撑的位置及结构拓扑有很大的影响，数值算例验证了刚度扩散方法在处理此类问题的有效性和灵活性。最后，对全部工作进行了总结，并对未来工作提出了展望。
[Abstract]:In this paper, based on stiffness diffusion method, several new optimization models dealing with collaborative optimization design of multi-component systems are proposed, which provide new ideas and methods for collaborative optimization design of multi-component systems. Firstly, the basic principle of stiffness diffusion method is introduced in detail, including radial basis function interpolation model, mathematical formula derivation and sensitivity analysis method. Some numerical examples are given to illustrate the characteristics of radial basis function interpolation and the rationality and effectiveness of the stiffness diffusion method in dealing with the optimization of truss structure layout and the optimal design of composite structures. Secondly, aiming at the problem of cooperative optimization design of member and continuum structure, this paper first presents a collaborative optimization design model of fixed member and continuum structure based on stiffness diffusion method. The stiffness of the member is diffused into the stiffness matrix of the continuum structure by the method of stiffness diffusion. The sensitivity analysis formula is derived and the validity of the proposed model is verified by a numerical example. On the basis of this, the cooperative optimization model of variable rod and continuum is proposed, and the optimization of the layout, size and topology of the continuum structure is realized at the same time. Thirdly, aiming at the problem of cooperative optimization design of elastomer and continuum structure, this paper proposes a cooperative optimization design model of topological fixed elastomer component and continuum structure, and divides the elastomer component into finite element meshes. The relation between displacement field of elastic body component and displacement field of braced structure is established by using radial basis function interpolation model in grid node coordinates, and stiffness of component is diffused into stiffness matrix of braced structure by means of stiffness diffusion method. Then, a cooperative optimization design model of component and continuum considering the topology optimization of elastomer components is proposed. Numerical examples show that the proposed method realizes the topology optimization of components at the same time. Layout optimization and topology optimization of continuum structure. Fourthly, by considering the bracing as an elastomer component moving in a special position, the cooperative optimization design of the structure support position and topology is realized by using the cooperative optimization design model of the elastomer component and the continuum structure proposed in this paper. In addition, considering the difficulty of construction in practical engineering, the cost constraints of support are added to the optimization model, and the optimization results under different cost constraints are obtained, which show that cost constraints have a great influence on the position and structure topology of the support. Numerical examples demonstrate the effectiveness and flexibility of the stiffness diffusion method in dealing with such problems. Finally, the whole work is summarized, and the prospect of future work is put forward.
【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】：TU318

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