發(fā)布時間：2018-06-27 03:27

  本文選題：數(shù)值計算 + 梯度光滑技術(shù)�。� 參考：《湖南大學》2016年博士論文

【摘要】：磁-力耦合問題是機械工程中常遇到的問題,以電磁成形為代表的涵蓋電磁和機械大變形分析的大規(guī)模復雜工程問題的數(shù)值模擬已引起工程和科研人員的日益關(guān)注。然而,傳統(tǒng)數(shù)值模擬計算方法在解決此類問題時漸顯乏力,其根本原因在于:基于非結(jié)構(gòu)網(wǎng)格的傳統(tǒng)有限元法前處理和計算均很簡便,且適于在復雜問題中應(yīng)用,但其存在對網(wǎng)格的依賴性和精度偏低的缺陷;而近二十年來發(fā)展的無網(wǎng)格法計算成本較高,難以用于求解大型復雜問題。如何利用非結(jié)構(gòu)網(wǎng)格的優(yōu)勢,構(gòu)造具備高精度,低計算成本以及低網(wǎng)格依賴性的數(shù)值算法成為解決此類問題的關(guān)鍵�；谶@一需求,本文提出了兼具有限元和無網(wǎng)格特性的穩(wěn)定節(jié)點積分算法,通過結(jié)構(gòu)場和電磁場計算對該方法的精度、效率、穩(wěn)定性、收斂率等特性進行了分析驗證,并將其用于電磁成形、電磁鉚接過程的數(shù)值模擬。具體工作為:1.提出了基于應(yīng)變梯度的時空間穩(wěn)定節(jié)點積分算法。為消除傳統(tǒng)節(jié)點光滑有限元法的不穩(wěn)定性,本文將應(yīng)變梯度項引入能量方程構(gòu)造出穩(wěn)定節(jié)點積分方法,并將其用于二維、三維彈性力學靜態(tài)和振動問題求解。該方法既保留了非結(jié)構(gòu)網(wǎng)格較低的前處理成本和計算簡便的優(yōu)勢,又有效地提高了有限元法的計算精度,并且具有類粒子法的特性,可以方便的進行后處理、數(shù)據(jù)傳遞或與其他算法耦合。通過對一系列標準算例和實際工程問題的分析,驗證了該方法的計算精度、效率、穩(wěn)定性和收斂性,結(jié)果表明:該方法得到高精度的計算結(jié)果,且很好地消除了傳統(tǒng)節(jié)點積分有限元法在動態(tài)分析中產(chǎn)生的奇異模式。2.提出了動態(tài)大變形分析中的穩(wěn)定節(jié)點積分方案。在動態(tài)大變形情況下,節(jié)點積分方法的不穩(wěn)定性更容易被激發(fā)而產(chǎn)生奇異的振蕩模式,且隱式彈性問題的穩(wěn)定項構(gòu)造方法在顯式非線性問題中不再直接適用。本文通過將積分域內(nèi)的應(yīng)變差異項引入內(nèi)力計算解決這一問題,構(gòu)建了適于顯式動態(tài)分析的節(jié)點積分方案。通過擠壓、碰撞等數(shù)值算例驗證了該方法的計算效果,結(jié)果顯示其特性包含:積分點數(shù)目少,在顯式問題中具有優(yōu)勢;良好的抗網(wǎng)格畸變能力,在結(jié)構(gòu)變形劇烈時仍可繼續(xù)計算;有效地提高了計算精度。3.構(gòu)造了電磁問題求解時的穩(wěn)定節(jié)點積分公式。對靜電、靜磁、穩(wěn)態(tài)電渦流和瞬態(tài)電渦流問題分別進行研究,在基于節(jié)點的光滑域內(nèi)對形函數(shù)的導數(shù)項進行一階泰勒展開,給出了每種情況下的穩(wěn)定節(jié)點積分方案。該方法基于線性三角形或四面體網(wǎng)格推導得到,其基本原理、方程最終形式及程序?qū)崿F(xiàn)均較簡單。通過多個標準算例驗證了所提方法的有效性。該方法提高了非結(jié)構(gòu)網(wǎng)格情況下電磁場的求解精度,在復雜問題分析中具有優(yōu)勢。4.根據(jù)所提出的節(jié)點積分算法,搭建了磁-力耦合的高效、自動化計算平臺,并將該平臺用于電磁成形和電磁鉚接過程的數(shù)值模擬。針對不同場模塊的特性,采用與之適應(yīng)的高效算法,并采用迭代耦合方式模擬出不同物理場之間的相互作用。對其中的網(wǎng)格更新過程采用加權(quán)彈性體法來實現(xiàn),該方法未增加額外的節(jié)點、未改變原有的網(wǎng)格拓撲關(guān)系,是一種簡便、有效、實用性強的方案。通過鋁合金材料的電磁脹形、電磁縮頸和電磁鉚接分析,從計算精度、效率和穩(wěn)定性等方面驗證了所提方法的實際效果。本文所搭建的計算平臺具有的優(yōu)勢包含:(1)不存在多個軟件之間的交互調(diào)用,消除了計算中的人工干預(yù),實現(xiàn)了模擬過程的自動化;(2)實現(xiàn)了多物理場之間的全耦合計算;(3)基于線性三角形網(wǎng)格,適于復雜結(jié)構(gòu)的分析;(4)基于節(jié)點的積分方法在數(shù)值模擬時得到較好的計算精度和計算效率,在復雜的工程問題中具有實際應(yīng)用價值。
[Abstract]:The problem of magnetic force coupling is a common problem in mechanical engineering. The numerical simulation of large-scale and complex engineering problems, including electromagnetic and mechanical large deformation analysis represented by electromagnetic forming, has attracted more and more attention from engineering and scientific researchers. However, the fundamental reason of the traditional numerical simulation method in solving such problems is weak. The traditional finite element method based on unstructured grid is simple and easy to use, and is suitable for complex problems, but its dependence on grid and accuracy is low. In the last twenty years, the computational cost of the meshless method is high, and it is difficult to solve large and complex problems. The key to solve such problems is to construct a numerical algorithm with high precision, low computational cost and low grid dependence. Based on this requirement, a stable node integration algorithm with both finite element and meshless characteristics is proposed. The precision, efficiency, stability and convergence rate of the method are calculated by the structure field and the electromagnetic field. The analysis and verification are carried out and applied to the numerical simulation of electromagnetic forming and electromagnetic riveting. 1. a spatio-temporal stable node integration algorithm based on strain gradient is proposed. In order to eliminate the instability of the traditional nodal smooth finite element method, the strain gradient term is introduced to the energy equation to construct a stable node integration method. The method is used to solve the static and vibration problems of two-dimensional, three-dimensional elastic mechanics. This method not only preserves the lower preprocessing costs and simple advantages of the unstructured grid, but also effectively improves the calculation precision of the finite element method, and has the characteristics of the particle like method, which can be easily processed, data transfer or other algorithms. Coupling. Through the analysis of a series of standard examples and practical engineering problems, the calculation accuracy, efficiency, stability and convergence of the method are verified. The results show that the method obtains high precision calculation results and well eliminates the dynamic large variation of the traditional node integration finite element method in the dynamic analysis of the singular mode.2.. In the case of dynamic large deformation, the instability of the node integration method is more easily excited to produce a singular oscillation mode, and the stability term construction method of implicit elastic problem is no longer directly applicable to the explicit nonlinear problem. In order to solve this problem, a node integral scheme suitable for explicit dynamic analysis is constructed. The calculation results of the method are verified by numerical examples such as extrusion and collision. The results show that the characteristics include: the number of points is few, and it has advantages in the explicit problem. The good ability to resist the distortion of the grid can continue to be calculated when the structure is strenuous. The calculation precision.3. is effectively improved and the stable node integral formula for solving the electromagnetic problem is constructed. The problems of static electricity, static magnetism, steady state eddy current and transient eddy current are studied respectively. The first order Taylor expansion of the derivative term of the shape function is carried out in the smooth domain based on the node, and the stable node integration scheme in each case is given. The method is derived from a linear triangle or tetrahedral mesh. The basic principle, the final form of the equation and the implementation of the program are simple. The effectiveness of the proposed method is verified by a number of standard examples. The method improves the accuracy of the electromagnetic field in the case of unstructured grids and has the advantage of.4. based on the advantages of the complex problem analysis. A high efficiency and automatic calculation platform for magnetic force coupling is built up, and the platform is used to simulate the process of electromagnetic forming and electromagnetic riveting. The efficient algorithm is adopted to adapt to the characteristics of different field modules and the interaction between different physical fields is simulated by iterative coupling. The process of grid updating is realized by the weighted elastic method. This method does not add additional nodes and does not change the original grid topology. It is a simple, effective and practical scheme. It is verified by the electromagnetic expansion, electromagnetic necking and electromagnetic riveting analysis of aluminum alloy materials from the aspects of calculation accuracy, efficiency and stability. The advantages of the method are as follows: (1) there is no interactive call between multiple software, the manual intervention in the calculation is eliminated, and the automation of the simulation process is realized; (2) the full coupling calculation between the multiple physical fields is realized; (3) based on the linear triangular mesh, it is suitable for the analysis of complex structures; (4) Node based integration method has good accuracy and efficiency in numerical simulation, and has practical application value in complex engineering problems.
【學位授予單位】：湖南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TG391

【相似文獻】

相關(guān)期刊論文 前4條

1 宋效林;周鋼;劉曉梅;;半定奇異系統(tǒng)的降階精細積分算法[J];東華大學學報(自然科學版);2008年06期

2 王先良;劉樂樂;吳章文;勾成俊;侯氫;;GPU加速劑量計算中微分卷積/積分算法的實現(xiàn)[J];核技術(shù);2013年05期

3 康國政;循環(huán)穩(wěn)定材料的棘輪行為:II.隱式應(yīng)力積分算法和有限元實現(xiàn)[J];工程力學;2005年03期

4 ;[J];;年期

相關(guān)會議論文 前1條

1 李江海;孫秦;黃建云;張永杰;;多層介質(zhì)電磁矢量單元的按層積分算法[A];2007年全國微波毫米波會議論文集（上冊）[C];2007年

相關(guān)博士學位論文 前3條

1 馮慧;時空間穩(wěn)定節(jié)點積分算法及其在磁—力耦合問題中的應(yīng)用研究[D];湖南大學;2016年

2 趙聃;汽車輕量化板材溫熱變形本構(gòu)積分算法研究[D];大連理工大學;2014年

3 彭奇;基于不變量空間的一般各向同性彈塑性本構(gòu)積分算法[D];武漢大學;2012年

相關(guān)碩士學位論文 前1條

1 王程飛;基于符號演算的分子積分算法研究和應(yīng)用[D];電子科技大學;2013年

，

本文編號：2072487