摘要
本文综述了边界元法的发展历史和研究现状,分析了奇异积分和几乎奇异积分计算的重要性,介绍了等价的边界积分方程。
基于前人的工作,归化出二维各向同性等截面直杆扭转的等价直接变量和间接变量无奇异边界积分方程,计算了端面剪应力。给出了二维各向异性等截面直杆扭转问题的基本解,归化出了二维各向异性等截面直杆扭转的等价直接变量和间接变量无奇异边界积分方程,端面剪应力的数值计算结果表明了本文算法的精确性。
给出平面正交各向异性单一介质坝基渗流问题的基本解,归化出平面正交各向异性单一介质坝基渗流的等价直接变量和间接变量无奇异边界积分方程,并应用其求解矩形坝基面的水头和法向流速,数值算例表明了本文算法的有效性。参照韦氏假设和动水压力的基本方程,归化出迎水坝面地震动水压力的等价间接变量和直接变量无奇异边界积分方程,动水压力的数值计算结果与韦氏解答一致。
利用二维静电场的等价间接变量无奇异边界积分方程,对传输线中非常关心的同轴线的特性阻抗进行了数值计算,分析了内外导体半径比与边界的电位势通量的关系。
引入了一种新的积分变换,有效地消除了边界元法在解决二维各向异性等截面直杆扭转问题和平面正交各向异性单一介质坝基渗流问题中所产生的边界层效应。数值算例表明,即使域内点非常的靠近边界,本文算法仍可取得理想的结果。
以温度场为例,基于一种新的思想,归化出第二类无奇异边界积分方程,数值结果表明,方程具有良好的收敛特性。
最后,对全文的研究成果进行了总结。对第二类无奇异边界积分方程理论的实际应用进行了展望。
The development and present situation of boundary element are surveyed. The important of singular and nearly singular is researched. Equivalent nonsingular boundary integral equations are introduced.
Based on the work of the predecessors, equivalent nonsingular boundary integral equations of two-dimensional isotropic uniform bar torsion are naturalized. The shear stress on the end is calculated. Fundamental solution of the anisotropic uniform bar torsion is present. Equivalent equations of anisotropic uniform bar torsion are also naturalized .The numerical results show an accurate algorithm.
Fundamental solution to plane orthotropic problem of seepage flow field with single media is given, equivalent equations of whose is naturalized. The numerical results of seepage parameters show an effective method. The same equivalent equations are naturalized in hydrodynamic pressure problem, which be referenced by W.t.'s premise and basic equations of hydrodynamic pressure. The parameters of hydrodynamic pressure are calculated the same to the W.t.'s.
With the equivalent equations of electric field, it made the numerical calculation to the characteristic impedance of coaxial line. Analysis is made to the rate of radius contrast to the potential flux on boundary.
A new integral transform is introduced. It is effectively eliminated the boundary layer effect introduced by the solution of two-dimensional isotropic uniform bar torsion problem and plane orthotropic problem of seepage flow field with single media with boundary element method. The numerical examples show an ideal result even though the inner point very closed to the boundary.
Take temperature field for example, the second-kind nonsingular equation is naturalized, based on a new idea. The numerical results show stable convergence.
Finally, it summarizes the research results and makes the outlook for the second-kind nonsingular boundary integral equations.
引文
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