等几何分析方法和比例边界等几何分析方法的研究及其工程应用

发布时间：2018-05-24 13:50

本文选题：等几何分析 + 比例边界有限元　；参考：《大连理工大学》2013年博士论文

【摘要】：本文基于等几何分析和比例边界有限元方法,研究开发了高精度、高效率的工程数值计算方法,将其应用于大坝-库水-地基系统的动力分析,并拓展至结构分析、电磁场分析和薄板弯曲和振动分析等工程问题的求解。等几何分析是近年来发展的一种新型的数值方法,旨在实现CAD和CAE的无缝统一。该方法将CAD中对几何形状进行精确描述的样条函数作为结构分析的形函数,可大大提高函数梯度场的计算精度,并在保持几何形状不变的前提下,方便地实现自适应的非通讯性细分操作。比例边界有限元方法是一种求解偏微分方程的半数值半解析解法,只需对求解区域的边界进行有限元离散,降低求解规模,但又无需基本解,特别适合于求解含有无限域、线弹性裂尖奇异应力场等工程问题。本文将等几何分析方法和比例边界有限元方法相结合,提出了新型的比例边界等几何分析方法,相比于等几何分析或者比例边界有限元,比例边界等几何分析方法的计算精度和计算效率进一步提高。因此将这种方法推广应用于实际工程中,将大大提高求解精度和效率。另外,此方法能和等几何分析方法进行无缝连接,利用等几何分析和比例边界等几何分析的耦合方法,建立了大坝-库水-无限地基时域动力分析的计算模型,全面考虑了大坝-库水、大坝-无限地基动力相互作用对大坝地震响应的影响。本文还将等几何分析、比例边界有限元方法、比例边界等几何分析的应用领域进行拓展,并对这些方法在实际应用中所遇到的若干理论和数值问题进行了深入研究,并提出了有效的解决方法。主要内容如下： (1)基于等几何分析和比例边界有限方法,提出了比例边界等几何分析方法。对弹性静、动力学以及电磁场问题分别推导了其离散方程和求解格式,并进行总结和比较。h-细分和p-细分过程仅需针对结构环向表面边界,在该方向上变量在相邻单元交界面处可达到较高的连续阶,而在径向解具有解析特性。相比于其他的数值方法,可达到更高的收敛速度。针对该方法,还研究了各类边界条件的施加策略。 (2)提出了大坝-库水-地基系统动力分析的等几何分析方法-比例边界等几何分析方法时域耦合计算模型,全面考虑了大坝-库水、大坝-无限地基动力相互作用的影响,并将其应用到高拱坝的地震动力分析中,为大坝的抗震安全评价提供重要参考依据。其中在大坝-库水动力相互作用分析中,考虑了库水可压缩性、库底淤沙对压力波的吸收、无限水域的辐射阻尼效应,并构造了压力-力转换矩阵,提高了流固耦合计算效率。在大坝-无限地基动力相互作用分析中,采用求解加速度脉冲响应函数的高效稳定算法,并构造了高效的加速度脉冲响应函数的离散策略和自适应策略,大大提高了相互作用力的计算精度和效率。利用该模型,分析了大坝-库水-地基动力相互作用对重力坝、拱坝系统地震响应的影响。 (3)针对比例边界有限元、等几何分析、比例边界等几何分析在新的应用领域拓展过程中遇到的若干理论和数值问题,提出了有效的处理方法。构造了新型的NURBS曲面的裁剪交点搜索算法及单元局部重构方式。相对于传统的以全域单元为搜索对象的搜索策略,新型的搜索策略则沿着裁剪曲线的切线方向逐一搜索,提高了搜索效率。提出了Lagrange乘子法解决重控制点问题和非齐次边值问题。发展了等几何分析在电磁场分析中的应用,对静电场问题和波导本征问题进行求解,显著地提高了计算效率和计算精度,对电容和波导等电子元件的设计具有重要参考意义。发展了等几何分析在薄板弯曲与振动分析中的应用,无需引入转角自由度便可满足C’连续的要求,显著地减少了计算自由度,并对稳定参数的取值进行了讨论。提出了相似中心由固定型扩展为移动型的处理方法,为比例边界有限元的进一步拓展,提供了有利条件。通过本论文的研究可看出,等几何分析方法、比例边界等几何分析方法在实际工程中具有广阔的应用前景,相关问题还需做更为广泛和深入的研究。
[Abstract]:Based on the equal geometric analysis and the proportional boundary finite element method, this paper develops a high precision and high efficiency numerical calculation method, and applies it to the dynamic analysis of the dam reservoir water foundation system, and extends to the structural analysis, the electromagnetic field analysis and the solution of the thin plate bending and vibration analysis.
Equal geometry analysis is a new numerical method developed in recent years, which aims to realize the seamless integration of CAD and CAE. This method uses the spline function which describes the geometric shape accurately as the shape function of the structural analysis, which can greatly improve the calculation precision of the function gradient field, and it is convenient to keep the geometric shape unchanged. The present self-adaptive non communication subdivision operation. The proportional boundary finite element method is a semi numerical semi analytic solution for solving partial differential equations. Only the finite element method is needed to solve the boundary of the solving region, and the solution size is reduced, but it does not need the basic solution. It is especially suitable for solving the engineering questions including the infinite domain, the singular stress field of the line elastic crack tip and so on. Question.
In this paper, a new geometric analysis method is proposed by combining the geometric analysis method with the proportional boundary finite element method. Compared with the geometric analysis or the proportional boundary finite element, the calculation precision and the calculation efficiency of the geometric analysis method are further higher than that of the equal geometric analysis or the proportional boundary finite element, so this method is popularized and applied to the actual work. In the process, the solution accuracy and efficiency will be greatly improved. In addition, the method can be connected seamlessly with the geometric analysis method, and the calculation model of the time domain dynamic analysis of the dam reservoir water infinite foundation is established by using the coupling method of geometric analysis and proportional boundary, such as the geometric analysis and the proportional boundary, and the dam reservoir water and the dynamic phase of the dam infinite foundation are considered in the whole. The influence of interaction on the seismic response of the dam. This paper also extends the application fields such as geometric analysis, proportional boundary finite element method, proportional boundary and other geometric analysis, and studies some theoretical and numerical problems encountered in practical applications, and puts forward effective solutions. Below:
(1) based on the equal geometric analysis and proportional boundary finite method, the geometric analysis method of proportional boundary is proposed. The discrete equation and the solution form are derived for the elastic static, dynamic and electromagnetic problems. The.H- subdivision and the p- subdivision process only need a needle to the surface boundary of the structure ring, and the variable in this direction is in the phase. A higher continuous order can be achieved at the interface of the adjacent unit, and the radial solution has an analytical characteristic. Compared with the other numerical methods, a higher convergence rate can be achieved. In this method, the application strategies of various boundary conditions are also studied.
(2) a time-domain coupling calculation model is proposed for the geometric analysis method of the dynamic analysis of the dam reservoir water foundation system dynamic analysis, such as the proportional boundary and the geometric analysis method, which comprehensively considers the influence of the dam reservoir water, the dynamic interaction of the dam and the infinite foundation, and applies it to the seismic dynamic analysis of the high arch dam, which provides the seismic safety evaluation for the dam. In the dam reservoir hydrodynamic interaction analysis, the compressibility of the reservoir water, the absorption of the sediment to the pressure wave and the radiation damping effect of the infinite water are considered in the analysis of dam reservoir hydrodynamic interaction, and the pressure force conversion matrix is constructed to improve the calculation efficiency of the fluid solid coupling. The efficient stability algorithm of the velocity impulse response function and the discrete strategy and adaptive strategy of the efficient acceleration impulse response function are constructed, and the calculation precision and efficiency of the interaction force are greatly improved. The effect of the dynamic interaction of dam, water and foundation on the seismic response of the gravity dam and the arch dam system is analyzed.
(3) aiming at some theoretical and numerical problems encountered in the development of new application fields such as proportional boundary finite element, equal geometric analysis, proportional boundary and other geometric analysis in the new application field, an effective processing method is proposed. A new NURBS surface cutting intersection search algorithm and unit local reconstruction method are constructed. The search strategy of the search object and the new search strategy are searched one by one along the tangent direction of the clipping curve to improve the search efficiency. The Lagrange multiplier method is proposed to solve the heavy control point problem and the non homogeneous boundary value problem. The application of the equal geometric analysis in the electromagnetic field analysis is developed, and the electrostatic field and the waveguide eigenproblem are solved. The solution has greatly improved the calculation efficiency and calculation accuracy. It has important reference significance for the design of electronic components such as capacitance and waveguide. The application of equal geometry analysis to the analysis of bending and vibration of thin plates has been developed. Without the introduction of angle freedom, it can satisfy the requirement of C 'continuity and significantly reduce the degree of freedom of calculation and to stabilize the parameters. The value is discussed. The method of processing similar center from fixed extension to movable type is proposed, which provides favorable conditions for further expansion of proportional boundary finite element.
Through the study of this paper, we can see that geometric analysis methods such as geometric analysis, proportional boundary and other geometric analysis methods have broad application prospects in practical engineering, and the related problems need to be more extensive and in-depth research.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU311.4

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