快速多极边界元法在薄板结构中的应用

基于Taylor级数多极展开研究了边界元快速多极算法(FM—BEM)，并将它应用于薄板结构。算例分析表明FM—BEM的计算时间和存储空间明显少于常规边界元迭代解法。随着问题规模的增大，这种优势将更加突出。     

Stability and Accuracy Analysis for Taylor Series Numerical Method

The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method.     

结构动力分析中时间积分方法进展

叙述了结构动力分析中时间积分方法的最新发展情况,对这一领域的基本原理和思想进行了总结,重点介绍一些新型计算方法的基本性质,为时间积分方法的进一步研究奠定基础。     

考虑横截面形状和几何尺寸的弹簧优化的两步式策略

针对弹簧优化设计中理论公式设计局限性大和有限元方法对多变量和多约束的优化设计效率低的问题,提出了一种考虑横截面形状和几何尺寸的弹簧优化的两步式策略。该策略利用密圈弹簧的理论计算公式结合多起点搜索方法对弹簧几何尺寸进行优化;采用有限元方法建立可以考虑截面形状变化的弹簧模型,用几何尺寸最优解为初值,采用零阶方法同时对截面形状和几何尺寸进行优化获得最优解。仿真结果表明:两步式策略能同时考虑横截面形状和几何尺寸进行弹簧优化设计,拓展了弹簧的设计范围;通过将两步式的优化策略结果与直接进行基于有限元方法的优化结果相比发现,优化时间减少了55.86%,两步式策略效率较高,降低了有限元优化的迭代次数;优化目标提高了14.31%,改善了出现局部最优解的情况。     

Fast Multipole BEM for 3-D Elastostatic Problems with Applications for Thin Structures

The fast multipole method (FMM) has been used to reduce the computing operations and memory requirements in large numerical analysis problems. In this paper, the FMM based on Taylor expansions is combined with the boundary element method (BEM) for three-dimensional elastostatic problems to solve thin plate and shell structures. The fast multipole boundary element method (FM-BEM)requires O(N) operations and memory for problems with N unknowns. The numerical results indicate that for the analysis of thin structures, the FM-BEM is much more efficient than the conventional BEM and the accuracy achieved is sufficient for engineering applications.     

基于力学思想的字体结构评价方法

汉字,是中华民族的伟大创造,是由笔画组成的结构体,所以科学合理的笔画结构,决定了字体的美观与否。本文引入力学领域中形心和惯性矩的概念,通过图像处理分析得到归一化后的字体图像形心和字体结构惯性矩,用这两个参数定量描述字体结构中重心和中宫的概念,为汉字字体结构提供评价方法和为汉字字体设计提供参考。     

谱载荷下疲劳裂纹扩展随机规律的实验研究

简要介绍了谱载荷下疲劳裂纹扩展试验的理论基础、方法和过程。讨论了各种数据处理方法对参数估计的影响,研究了疲劳裂纹扩展的随机规律。由试验得到的疲劳裂纹扩展试验数据估计了裂纹扩展方程的参数,计算出结构可靠度曲线,通过对试验结果的分析难证了以下结论：以时间为参量的裂纹扩展随机过程模型和以裂纹长度为参量的模型在一定条件下是统一的;数据处理方法的选择与可靠性分析的结果有密切的联系;裂纹扩展寿命受裂纹扩展队机