【作者】 张艳岗；

【导师】 苏铁熊；

【作者基本信息】 中北大学 ， 机动武器系统工程， 2014， 博士

【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。更多还原

【Abstract】 Traditional structural optimization is carried out under static load, while mechanicalstructure of engineering practice was generally under locally dynamic load, therefore theresults based on static structure optimization design method cannot meet the requirements ofthe structural dynamic performance. Due to the time-related dynamic constraint of the directdynamic response optimization technology was difficult to deal with, the direct optimizationcalculation of dynamic response is large scale and difficult to converge, so it is not feasiblefor structural dynamic response optimization design directly in engineering applications.Therefore, it is considered to transform dynamic load into equivalent static load. At present,the Equivalent Static Load method based on displacement, transforms dynamic load intostatic load via equivalent displacement, and further transforms the structure dynamic responseproblem into structure static response problem. This method takes the maximumdisplacement point as the equivalent transformation time point, without considering thedynamic response of the maximum stress time point, and cannot fully reflect the dynamicperformance of the structure, and the equivalent transformation critical time point is difficultto identify. Whatever, the equivalent static load method based on displacement is short incomplex computation and insufficient optimization inefficient, which leads to poorpracticability? In addition the current dynamic response optimization is based ondisplacement, ignoring the effects of stress response on the structural dynamic performance.Aiming at the problem that the critical time point at which the structure dynamic loadequivalent transformation is taken was difficult to identify, a method based on discretizingthe solution space of the dynamic response by the spectral element method to identify the critical time point is presented. The paper utilizes the discrete by spectral element method andthe high-precision of the Gauss–Legendre–Lobatto (GLL) point interpolation, calculatesthe spectral element discrete solution space of the structure dynamic response (stressresponse and displacement response included) resulting from the modal superposition methodcalculation, and obtain a high-precision interpolation function of dynamic response timehistory, by Lagrange interpolation at GLL point, constructed a mathematical model toidentify the structure of the critical time point under dynamic load, and get the absolutemaximum structure dynamic response value point by global optimization algorithm (DIRECTmethod), called critical time point. Finally, a124-plane truss and cantilever beam were takenas examples to demonstrate the effectiveness of this method.Aiming at the complex optimization calculation and poor practicability of the EquivalentStatic Load method based on displacement, a method in which the dynamic load istransformed into static based on energy principle is presented. This method is based on theconservation of the energy before and after the load equivalent, constructs a mathematicalmodel of the transformation of the dynamic load into static load, and obtains the equivalentstatic load set by global optimization algorithm (DIRECT method) eventually. The124planetruss was analyzed as an example, to confirm the validity of this method.Aiming at the insufficiency of simply considering the displacement response when thestructure is dynamic optimized by using the Equivalent Static Load method based ondisplacement, a structure dynamic optimized design method based on system response ispresented. The structure is optimized with the displacement response and the stress responsewhich are generated when the structure is under dynamic load, as constraint functions of theoptimization model, and the static load set, which is generated by equivalently transformationat critical time point identified from the point of stress and displacement, as the external loadcondition of structure dynamic optimization. A circular hollow section beam, a3-trussstructure, and a10-truss structure were taken as examples and compared with the literatures.The results show that, the optimization result obtained by this method is more accurate. A diesel engine piston was used as the application study in this paper. The thermalboundary condition of the piston was corrected by the test results, and the temperature ofeach node of the piston was got by the finite element method. The dynamic response solutionspace of the piston was got by the thermo-mechanical coupling static analysis and thetransient kinetic analysis of the piston. The method to identify the critical time point and theEquivalent Load method based on energy principle presented in this paper were used totransform the dynamic load into static load equivalently at the critical time point, and then thestructure optimization design method based on system response was applied. Theoptimization of the dynamic response of the piston was achieved eventually, and achievedgood results.By the investigation of the energy principle based Equivalent Static Load method and itsapplication for the dynamic response optimization in the paper, breakthroughs in the areas ofthe identification of critical time point of the transformation of equivalent load, thetransformation of dynamic load into static load based on energy principle and the structuredynamic response optimization design based on system response, are made, and a series ofconclusion and results with theoretical significance and practical value are received. Thepaper expands the scope of the theoretical study of Equivalent Load method, and opens a newway of theoretical study on dynamic response optimization theory.更多还原