本文選題：能量原理 + 等效靜態(tài)載荷法��； 參考：《中北大學(xué)》2014年博士論文

【摘要】：傳統(tǒng)的結(jié)構(gòu)優(yōu)化設(shè)計(jì)是靜態(tài)載荷下的優(yōu)化設(shè)計(jì)，而工程實(shí)際中的機(jī)械結(jié)構(gòu)普遍承受動態(tài)載荷作用，因此靜態(tài)優(yōu)化設(shè)計(jì)的結(jié)果已不能滿足結(jié)構(gòu)動態(tài)性能的要求。而直接進(jìn)行動態(tài)響應(yīng)優(yōu)化設(shè)計(jì)時(shí)，由于與時(shí)間相關(guān)的動態(tài)約束處理非常困難，往往導(dǎo)致計(jì)算規(guī)模大且難以收斂，所以該方法在工程實(shí)際應(yīng)用中尚不可行。因此，人們考慮將動態(tài)載荷等效轉(zhuǎn)化為靜態(tài)載荷。目前基于位移的等效靜態(tài)載荷法，是通過位移場等效將動態(tài)載荷轉(zhuǎn)化為靜態(tài)載荷，進(jìn)而將結(jié)構(gòu)動態(tài)響應(yīng)優(yōu)化問題轉(zhuǎn)化為靜態(tài)響應(yīng)優(yōu)化問題，但該方法是以最大位移點(diǎn)為等效轉(zhuǎn)化時(shí)間點(diǎn)，沒有考慮最大應(yīng)力點(diǎn)時(shí)刻的動態(tài)響應(yīng)，不能全面反映結(jié)構(gòu)的動態(tài)性能，而等效轉(zhuǎn)化關(guān)鍵時(shí)間點(diǎn)難以識別。同時(shí)基于位移等效靜態(tài)載荷法存在計(jì)算復(fù)雜、優(yōu)化效率低的問題，導(dǎo)致工程實(shí)用性差。另外，目前的結(jié)構(gòu)動態(tài)響應(yīng)優(yōu)化是以位移響應(yīng)為基礎(chǔ)的，忽略了應(yīng)力響應(yīng)對結(jié)構(gòu)動態(tài)性能的影響。 論文針對目前結(jié)構(gòu)動態(tài)載荷等效靜態(tài)轉(zhuǎn)化時(shí)關(guān)鍵時(shí)間點(diǎn)難以識別的問題，提出了一種動態(tài)響應(yīng)解空間譜元離散的關(guān)鍵時(shí)間點(diǎn)識別方法。應(yīng)用譜元法離散以及在高斯-勒讓德-羅巴托(GLL)點(diǎn)插值的高精度優(yōu)勢，將模態(tài)疊加法計(jì)算得到的結(jié)構(gòu)動態(tài)響應(yīng)（包括應(yīng)力響應(yīng)和位移響應(yīng)）解空間進(jìn)行譜元離散，并在GLL點(diǎn)進(jìn)行Lagrange插值，得到了動態(tài)響應(yīng)時(shí)間歷程的高精度插值函數(shù)，構(gòu)建了動態(tài)載荷作用下結(jié)構(gòu)關(guān)鍵時(shí)間點(diǎn)識別的數(shù)學(xué)模型，并利用全局優(yōu)化算法（DIRECT法）得到結(jié)構(gòu)動態(tài)響應(yīng)的絕對極大值點(diǎn)，即關(guān)鍵時(shí)間點(diǎn)，并以124桿平面桁架和懸臂梁為算例，驗(yàn)證了本文方法的有效性。 論文針對基于位移等效靜態(tài)載荷法的優(yōu)化計(jì)算復(fù)雜、工程實(shí)用性差的問題，提出了一種基于能量等效的動態(tài)載荷等效靜態(tài)轉(zhuǎn)化方法�；谳d荷等效前后結(jié)構(gòu)能量守恒的原理，通過在關(guān)鍵時(shí)間點(diǎn)構(gòu)建動態(tài)載荷等效靜態(tài)轉(zhuǎn)化的數(shù)學(xué)模型，并采用全局優(yōu)化算法（DIRECT法）搜索得到了關(guān)鍵時(shí)間點(diǎn)的等效載荷集。同樣以124桿平面桁架為算例進(jìn)行分析，驗(yàn)證了本文方法的有效性。 論文針對基于位移等效靜態(tài)載荷法在進(jìn)行結(jié)構(gòu)動態(tài)優(yōu)化時(shí)，單純考慮位移響應(yīng)的不足，提出了一種基于系統(tǒng)響應(yīng)的結(jié)構(gòu)動態(tài)優(yōu)化設(shè)計(jì)方法。在構(gòu)建結(jié)構(gòu)優(yōu)化模型時(shí)，同時(shí)考慮動態(tài)載荷作用的結(jié)構(gòu)位移響應(yīng)和應(yīng)力響應(yīng)，將分別從最大應(yīng)力、最大位移角度識別的關(guān)鍵時(shí)間點(diǎn)等效轉(zhuǎn)化得到的靜態(tài)載荷集，作為結(jié)構(gòu)動態(tài)優(yōu)化的外載荷條件，進(jìn)行結(jié)構(gòu)優(yōu)化設(shè)計(jì)。并以圓形中空截面梁、3桿桁架結(jié)構(gòu)、10桿桁架結(jié)構(gòu)等算例為研究對象進(jìn)行驗(yàn)證，通過與文獻(xiàn)分析對比，表明本文得到的優(yōu)化結(jié)果更加精確。 論文以某柴油機(jī)活塞為應(yīng)用對象，結(jié)合試驗(yàn)結(jié)果修正了活塞的熱邊界條件，利用有限元法仿真分析得到了活塞各個節(jié)點(diǎn)的溫度；開展了活塞熱機(jī)耦合靜力學(xué)分析和瞬態(tài)動力學(xué)分析，得到了活塞動態(tài)響應(yīng)解空間，分別應(yīng)用本文提出的關(guān)鍵時(shí)間點(diǎn)識別方法和基于能量原理的等效載荷法進(jìn)行活塞在關(guān)鍵時(shí)間點(diǎn)的動態(tài)載荷等效靜態(tài)轉(zhuǎn)化，并應(yīng)用基于系統(tǒng)響應(yīng)的結(jié)構(gòu)優(yōu)化設(shè)計(jì)方法，實(shí)現(xiàn)了活塞的動態(tài)響應(yīng)優(yōu)化設(shè)計(jì)，取得了良好的效果。 本文研究了基于能量原理的等效靜態(tài)載荷法及其在結(jié)構(gòu)動態(tài)響應(yīng)優(yōu)化中的應(yīng)用，在載荷等效轉(zhuǎn)化關(guān)鍵時(shí)間點(diǎn)識別、基于能量原理的動態(tài)載荷等效靜態(tài)轉(zhuǎn)化、基于系統(tǒng)響應(yīng)的結(jié)構(gòu)動態(tài)響應(yīng)優(yōu)化設(shè)計(jì)三方面取得了突破，獲得了一系列具有理論意義和工程實(shí)用價(jià)值的結(jié)論與成果，拓展了等效靜態(tài)載荷法的理論研究范疇，為動態(tài)響應(yīng)優(yōu)化相關(guān)理論研究開辟了新的途徑。
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TH122

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本文編號：1906882