基于关键时间点的能量等效静态载荷法及结构动态响应优化研究

发布时间：2018-05-18 19:14

本文选题：能量原理 + 等效静态载荷法　；参考：《中北大学》2014年博士论文

【摘要】：传统的结构优化设计是静态载荷下的优化设计，而工程实际中的机械结构普遍承受动态载荷作用，因此静态优化设计的结果已不能满足结构动态性能的要求。而直接进行动态响应优化设计时，由于与时间相关的动态约束处理非常困难，往往导致计算规模大且难以收敛，所以该方法在工程实际应用中尚不可行。因此，人们考虑将动态载荷等效转化为静态载荷。目前基于位移的等效静态载荷法，是通过位移场等效将动态载荷转化为静态载荷，进而将结构动态响应优化问题转化为静态响应优化问题，但该方法是以最大位移点为等效转化时间点，没有考虑最大应力点时刻的动态响应，不能全面反映结构的动态性能，而等效转化关键时间点难以识别。同时基于位移等效静态载荷法存在计算复杂、优化效率低的问题，导致工程实用性差。另外，目前的结构动态响应优化是以位移响应为基础的，忽略了应力响应对结构动态性能的影响。论文针对目前结构动态载荷等效静态转化时关键时间点难以识别的问题，提出了一种动态响应解空间谱元离散的关键时间点识别方法。应用谱元法离散以及在高斯-勒让德-罗巴托(GLL)点插值的高精度优势，将模态叠加法计算得到的结构动态响应（包括应力响应和位移响应）解空间进行谱元离散，并在GLL点进行Lagrange插值，得到了动态响应时间历程的高精度插值函数，构建了动态载荷作用下结构关键时间点识别的数学模型，并利用全局优化算法（DIRECT法）得到结构动态响应的绝对极大值点，即关键时间点，并以124杆平面桁架和悬臂梁为算例，验证了本文方法的有效性。论文针对基于位移等效静态载荷法的优化计算复杂、工程实用性差的问题，提出了一种基于能量等效的动态载荷等效静态转化方法。基于载荷等效前后结构能量守恒的原理，通过在关键时间点构建动态载荷等效静态转化的数学模型，并采用全局优化算法（DIRECT法）搜索得到了关键时间点的等效载荷集。同样以124杆平面桁架为算例进行分析，验证了本文方法的有效性。论文针对基于位移等效静态载荷法在进行结构动态优化时，单纯考虑位移响应的不足，提出了一种基于系统响应的结构动态优化设计方法。在构建结构优化模型时，同时考虑动态载荷作用的结构位移响应和应力响应，将分别从最大应力、最大位移角度识别的关键时间点等效转化得到的静态载荷集，作为结构动态优化的外载荷条件，进行结构优化设计。并以圆形中空截面梁、3杆桁架结构、10杆桁架结构等算例为研究对象进行验证，通过与文献分析对比，表明本文得到的优化结果更加精确。论文以某柴油机活塞为应用对象，结合试验结果修正了活塞的热边界条件，利用有限元法仿真分析得到了活塞各个节点的温度；开展了活塞热机耦合静力学分析和瞬态动力学分析，得到了活塞动态响应解空间，分别应用本文提出的关键时间点识别方法和基于能量原理的等效载荷法进行活塞在关键时间点的动态载荷等效静态转化，并应用基于系统响应的结构优化设计方法，实现了活塞的动态响应优化设计，取得了良好的效果。本文研究了基于能量原理的等效静态载荷法及其在结构动态响应优化中的应用，在载荷等效转化关键时间点识别、基于能量原理的动态载荷等效静态转化、基于系统响应的结构动态响应优化设计三方面取得了突破，获得了一系列具有理论意义和工程实用价值的结论与成果，拓展了等效静态载荷法的理论研究范畴，为动态响应优化相关理论研究开辟了新的途径。
[Abstract]:The traditional structural optimization design is the optimal design under static load, and the mechanical structure in the engineering practice generally bears the dynamic load. Therefore, the result of static optimization design can not meet the requirements of the dynamic performance of the structure. Therefore, it is not feasible in the practical application of the engineering. Therefore, the dynamic load is considered to be equivalent to the static load. At present, the equivalent static load method based on displacement is used to transform the dynamic load into static load by the equivalent displacement field, and then the dynamic response of the structure is optimized. The problem is transformed into a static response optimization problem, but the method uses the maximum displacement point as the equivalent transformation time point and does not consider the dynamic response of the maximum stress point. It can not fully reflect the dynamic performance of the structure, but the critical time point of the equivalent transformation is difficult to identify. Meanwhile, the displacement equivalent static load method has the complexity and the optimization efficiency based on the displacement equivalent static load method. In addition, the current structural dynamic response optimization is based on the displacement response and neglects the effect of the stress response on the dynamic performance of the structure.
In view of the problem that the critical time points are difficult to identify in the current dynamic load equivalent static transformation, a key time point identification method for dynamic response spatial spectral element discretization is proposed. The high precision advantage of the discrete spectral element method and the Gauss Legendre - Robert (GLL) point interpolation is used to calculate the junction of the modal superposition method. The dynamic response (including stress response and displacement response) is discrete, and the Lagrange interpolation is carried out at the GLL point. The high precision interpolation function of the dynamic response time history is obtained. The mathematical model of the key time point identification of the structure under the dynamic load is constructed, and the structure dynamics is obtained by the global optimization algorithm (DIRECT method). The absolute maximum point of the response, that is, the critical time point, is verified by the example of 124 bar plane truss and cantilever beam.
Based on the problem of complex optimization calculation based on displacement equivalent static load method and poor engineering practicability, a dynamic load equivalent static transformation method based on energy equivalent is proposed. Based on the principle of energy conservation of the structure before and after the load equivalent, the mathematical model of the equivalent static transformation of dynamic load is constructed at the critical time point. The global optimization algorithm (DIRECT) is used to find the equivalent load set at the critical time point. The 124 bar truss is also used as an example to verify the effectiveness of the proposed method.
In order to optimize the structure dynamic optimization based on the displacement equivalent static load method, a dynamic optimization design method based on the response of the system is proposed. When the structure optimization model is built, the structural displacement response and stress response of the dynamic load are taken into consideration, and the maximum stress will be from the maximum stress respectively. The key time point of the maximum displacement angle is equivalent to the static load set, which is used as the external load condition of the dynamic optimization of the structure, and the structural optimization design is carried out. The example of the circular hollow cross section beam, the 3 bar truss structure and the 10 bar truss structure is verified, and the advantages of this paper are compared with the literature analysis. The result is more accurate.
Taking the piston of a diesel engine as the application object, the thermal boundary condition of the piston is corrected by the test results. The temperature of each node of the piston is obtained by the finite element simulation analysis. The static analysis and transient dynamics analysis of the piston hot machine are carried out, and the dynamic response space of the piston is obtained. The key time point identification method and the equivalent load method based on the energy principle are used to perform the equivalent static load transformation of the piston at the critical time point, and the optimal design method based on the structural response based on the system response is applied to achieve the optimal design of the dynamic response of the piston, and good results have been achieved.
In this paper, the equivalent static load method based on energy principle and its application in structural dynamic response optimization are studied. In the key time point identification of load equivalent transformation, dynamic load equivalent static transformation based on energy principle, three aspects of structural dynamic response optimization design based on system response have been achieved, and a series of have been obtained. The conclusions and results of theoretical significance and practical value of engineering have expanded the theoretical research category of the equivalent static load method and opened a new way for the study of dynamic response optimization.
【学位授予单位】：中北大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH122

【相似文献】