摘 要
机械结构的拓扑优化是现代工程设计中的重要研究方向，旨在通过优化材料分布实现结构性能的最大化。随着复杂工程问题的日益增多，传统设计方法已难以满足高性能、轻量化和多功能化的需求。本研究以提升机械结构性能为目标，基于先进的数值算法与理论模型，提出了一种结合多目标优化策略和改进密度法的新型拓扑优化框架。该框架能够有效解决多工况约束下的结构优化问题，并在保证计算效率的同时提高解的质量。研究中引入了自适应滤波技术以减少棋盘格现象，同时通过灵敏度分析改进了梯度计算方法，显著提升了优化过程的收敛速度。通过对典型机械结构（如承载梁、连接件及复杂壳体）的案例分析，验证了所提方法在减轻重量、增强刚度和改善应力分布方面的优越性。
关键词：拓扑优化 多目标优化 改进密度法
Abstract
Topological optimization of mechanical structure is an important research direction in modern engineering design, aiming to maximize the structural performance by optimizing the material distribution. With the increasing number of complex engineering problems, the traditional design methods are difficult to meet the needs of high performance, lightweight and multifunctional. In this study, we propose a novel topological optimization fr amework combining multi-ob jective optimization strategy and improved densitometry, based on advanced numerical algorithms and theoretical models. This fr amework can effectively solve the structural optimization problem under multiple working condition constraints, and improve the quality of solutions while ensuring the computational efficiency. Adaptive filtering technique is introduced to reduce the checkerboard phenomenon, and the gradient calculation method is improved through sensitivity analysis, which significantly improves the convergence rate of the optimization process. Case analysis of typical mechanical structures (e. g., bearing beams, connections and complex shells) demonstrates the superiority of the proposed method in reducing weight, enhancing stiffness and improving stress distribution.
Keyword:Topology Optimization Multi-ob jective Optimization Improved Density Method
目 录
引言 1
1拓扑优化理论基础研究 1
1.1拓扑优化的基本概念 1
1.2拓扑优化的数学模型构建 2
1.3常用拓扑优化算法综述 2
1.4拓扑优化在机械结构中的应用现状 3
2机械结构性能分析方法 3
2.1机械结构性能的关键指标定义 3
2.2结构应力与变形的数值模拟方法 3
2.3动态性能分析的技术手段 4
2.4性能分析结果的验证与评估 4
3拓扑优化驱动的结构设计改进 5
3.1拓扑优化目标的设定原则 5
3.2约束条件对优化结果的影响 5
3.3多工况下的结构优化策略 6
3.4优化后结构的可制造性分析 6
4性能提升的具体实现路径 6
4.1材料选择对性能的影响研究 7
4.2轻量化设计与强度保持的平衡 7
4.3新型结构形式的探索与验证 7
4.4实际案例中的性能提升效果分析 8
结论 8
参考文献 10
致谢 11
