时空间稳定节点积分算法及其在磁—力耦合问题中的应用研究

发布时间：2018-06-27 03:27

本文选题：数值计算 + 梯度光滑技术　；参考：《湖南大学》2016年博士论文

【摘要】：磁-力耦合问题是机械工程中常遇到的问题,以电磁成形为代表的涵盖电磁和机械大变形分析的大规模复杂工程问题的数值模拟已引起工程和科研人员的日益关注。然而,传统数值模拟计算方法在解决此类问题时渐显乏力,其根本原因在于:基于非结构网格的传统有限元法前处理和计算均很简便,且适于在复杂问题中应用,但其存在对网格的依赖性和精度偏低的缺陷;而近二十年来发展的无网格法计算成本较高,难以用于求解大型复杂问题。如何利用非结构网格的优势,构造具备高精度,低计算成本以及低网格依赖性的数值算法成为解决此类问题的关键。基于这一需求,本文提出了兼具有限元和无网格特性的稳定节点积分算法,通过结构场和电磁场计算对该方法的精度、效率、稳定性、收敛率等特性进行了分析验证,并将其用于电磁成形、电磁铆接过程的数值模拟。具体工作为:1.提出了基于应变梯度的时空间稳定节点积分算法。为消除传统节点光滑有限元法的不稳定性,本文将应变梯度项引入能量方程构造出稳定节点积分方法,并将其用于二维、三维弹性力学静态和振动问题求解。该方法既保留了非结构网格较低的前处理成本和计算简便的优势,又有效地提高了有限元法的计算精度,并且具有类粒子法的特性,可以方便的进行后处理、数据传递或与其他算法耦合。通过对一系列标准算例和实际工程问题的分析,验证了该方法的计算精度、效率、稳定性和收敛性,结果表明:该方法得到高精度的计算结果,且很好地消除了传统节点积分有限元法在动态分析中产生的奇异模式。2.提出了动态大变形分析中的稳定节点积分方案。在动态大变形情况下,节点积分方法的不稳定性更容易被激发而产生奇异的振荡模式,且隐式弹性问题的稳定项构造方法在显式非线性问题中不再直接适用。本文通过将积分域内的应变差异项引入内力计算解决这一问题,构建了适于显式动态分析的节点积分方案。通过挤压、碰撞等数值算例验证了该方法的计算效果,结果显示其特性包含:积分点数目少,在显式问题中具有优势;良好的抗网格畸变能力,在结构变形剧烈时仍可继续计算;有效地提高了计算精度。3.构造了电磁问题求解时的稳定节点积分公式。对静电、静磁、稳态电涡流和瞬态电涡流问题分别进行研究,在基于节点的光滑域内对形函数的导数项进行一阶泰勒展开,给出了每种情况下的稳定节点积分方案。该方法基于线性三角形或四面体网格推导得到,其基本原理、方程最终形式及程序实现均较简单。通过多个标准算例验证了所提方法的有效性。该方法提高了非结构网格情况下电磁场的求解精度,在复杂问题分析中具有优势。4.根据所提出的节点积分算法,搭建了磁-力耦合的高效、自动化计算平台,并将该平台用于电磁成形和电磁铆接过程的数值模拟。针对不同场模块的特性,采用与之适应的高效算法,并采用迭代耦合方式模拟出不同物理场之间的相互作用。对其中的网格更新过程采用加权弹性体法来实现,该方法未增加额外的节点、未改变原有的网格拓扑关系,是一种简便、有效、实用性强的方案。通过铝合金材料的电磁胀形、电磁缩颈和电磁铆接分析,从计算精度、效率和稳定性等方面验证了所提方法的实际效果。本文所搭建的计算平台具有的优势包含:(1)不存在多个软件之间的交互调用,消除了计算中的人工干预,实现了模拟过程的自动化;(2)实现了多物理场之间的全耦合计算;(3)基于线性三角形网格,适于复杂结构的分析;(4)基于节点的积分方法在数值模拟时得到较好的计算精度和计算效率,在复杂的工程问题中具有实际应用价值。
[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.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TG391

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