起重机桁架臂顶节局部拓扑优化研究

发布时间：2018-04-27 21:08

本文选题：拓扑优化 + 铰点布局优化　；参考：《大连理工大学》2012年硕士论文

【摘要】：桁架臂顶节局部结构的拓扑优化设计问题,是当前桁架类吊臂设计中所面临的一项关键性问题。合理的顶节局部结构的材料布局形式,不仅能够充分发挥材料的力学性能、减轻结构重量,还能有效的传递载荷、提高桁架臂整体的抗屈曲能力,进而提高桁架类起重机整机的起重性能。桁架臂顶节结构复杂,工况繁多,直接运用常规的拓扑优化思想很难获得最佳的结构布局。针对这一问题文中提出了一种新的优化设计方法,其总体思路是：首先,基于弹性稳定性思想确定满足臂架最小屈曲储存应变能下合理的受力铰点位置。其次,运用基于灰色理论的改进的折中规划思想完成多工况下顶节局部拓扑优化设计。最后,针对拓扑优化中数值不稳定性现象,引入避免灰色材料边界的非线性密度过滤技术予以消除。论文的主要研究工作和成果如下： (1)基于弹性稳定约束的桁架臂顶节铰点布局优化。运用铁摩辛柯弹性稳定性理论,将桁架臂结构简化成铁摩辛柯梁形式；在此基础上,以最小屈曲储存应变能为目标函数建立数学模型,运用遗传算法对桁架臂顶节铰点布局优化问题进行求解。 (2)基于SIMP法的连续体结构单工况拓扑优化。在材料密度插值理论的基础上,建立单工况下变密度插值法最小柔度问题的拓扑优化数学模型并推导出优化准则算法。 (3)基于SIMP法的桁架臂顶节多工况拓扑优化。基于SIMP变密度的拓扑优化思想,运用折中规划法建立桁架臂顶节结构静态多工况下多刚度拓扑优化数学模型。基于灰色理论的专家评价思想对上述算法进行改进,以获得合理的目标函数权重消除主观因素的影响。利用OptiStruct软件对优化模型进行求解,以获得静态多工况下最优拓扑。 (4)避免灰色材料边界的非线性网格过滤技术。为避免诸如棋盘格式和网格依赖性等数值不稳定现象、确保优化结果的可制造性,常需要在拓扑优化中引入过滤技术。然而,运用常规的过滤技术时,拓扑结果中会出现灰色材料边界现象以致难以用于加工制造。非线性密度过滤技术(如基于Heaviside函数过滤技术),能有效避免这一现象,但不能保证迭代过程材料体积的守恒性导致震荡现象。基于Heaviside函数的体积守恒过滤技术能够保证迭代体积守恒性,确保了优化的高效性和迭代的稳定性。提出了一种体积守恒非线性密度过滤函数,通过工程实例验证其算法是合理、有效的,较上述体积守恒非线性过滤函数表达式更为简洁、收敛性更好,并可获得材料边界清晰的拓扑结果。
[Abstract]:The topology optimization of the local structure of the truss arm top joint is a key problem in the design of the truss boom. The reasonable material layout of the local structure can not only give full play to the mechanical properties of the material, reduce the weight of the structure, but also effectively transfer the load and improve the overall buckling resistance of the truss arm. Thus, the lifting performance of the truss crane is improved. The structure of the top joint of the truss arm is complex and the working conditions are various. It is difficult to obtain the optimal structure layout by using the conventional topology optimization idea directly. A new optimal design method is proposed in this paper. The main ideas are as follows: firstly, based on the elastic stability theory, a reasonable position of the pivot point satisfying the minimum buckling storage strain energy of the boom is determined. Secondly, the local topology optimization design of the top node under multiple working conditions is completed by using the improved compromise planning idea based on the grey theory. Finally, the nonlinear density filtering technique is introduced to eliminate the numerical instability in topology optimization. The main research work and results are as follows: 1) the optimization of the hinge point layout at the top of the truss arm based on elastic stability constraints. In this paper, the truss arm structure is simplified into the form of iron friction beam by using Temocco elastic stability theory, and the mathematical model is established based on the minimum buckling stored strain energy as the objective function. Genetic algorithm (GA) is used to solve the optimization problem of the hinge point layout at the top of the truss arm. 2) Topology optimization of continuum structure under single working condition based on SIMP method. Based on the theory of material density interpolation, the topological optimization mathematical model of minimum flexibility problem of variable density interpolation method under single working condition is established and the optimization criterion algorithm is derived. 3) Topology optimization of truss arm top joint based on SIMP method. Based on the idea of topological optimization of SIMP variable density, a mathematical model of topology optimization of truss arm joints under static condition and multiple working conditions is established by means of compromise programming method. The expert evaluation idea based on grey theory is used to improve the above algorithm in order to get a reasonable weight of objective function to eliminate the influence of subjective factors. The optimization model is solved by OptiStruct software in order to obtain the optimal topology under static and multi-working conditions. (4) Non-linear mesh filtering technique to avoid gray material boundary. In order to avoid numerical instability such as chessboard format and grid dependency and ensure the manufacturability of optimization results filtering techniques are often introduced into topology optimization. However, using conventional filtering techniques, grey material boundary phenomena will occur in topological results, which makes it difficult to be used in processing and manufacturing. The nonlinear density filtering technique, such as filter based on Heaviside function, can effectively avoid this phenomenon, but it can not guarantee the conservation of material volume in the iterative process. The volume conservation filtering technique based on Heaviside function can guarantee the iterative volume conservation and ensure the efficiency of optimization and the stability of iteration. A novel nonlinear density filtering function for volume conservation is proposed. The algorithm is proved to be reasonable and effective by an engineering example, and it is more concise and convergent than the expression of the volume conservation nonlinear filter function mentioned above. The topological results with clear material boundary can be obtained.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH21

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