边界元法中的改进等参变换
The Improved Isoparametric Transformation in BEM
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摘要: 首先考察三维边界元法中八结点等参单元边中结点的敏感性,指出对于常规等参变换计算,边中结点同有限元计算情形一样,仍必须遵守位于相邻角点间距离的三分之一内的建议,且限制应更严格,才能保证计算的有效性.其次,将改进等参变换引入到边界元法,并解决了相应的奇异积分处理等问题,提出了一个比常规等参变换时更加一般的坐标变换关系式.最后,对于立方块受单向拉伸和纯弯曲两种情况作了计算,结果表明,在边界元法中,改进等参变换的引入,使得计算具有更大的适应性.Abstract: The so-called "Subjectivity Geometry" herein is a course for studying the relationship between the abstracted object configuration and its observed record by means of mathematical methods and described by matlieinatical language. There are many features differing from the common geometry when the effects of the subjectivity(such as the position of the observer, the functions of the visual system of human) are taken into account during the observing-recording process. In this paper, some basic assumptions are made; spherieal observing record is suggested: the fundamental relationship between the abstracted object configuration and its corresponding observed record is studied and an example of apiriication of the above theory is presented. We anticipate that the study of subjectivity geometry will influencc, or will be associated with the study of physiology of the visual system, applied optics etc., and will be useful in surveying, pilotage and imitative biology, etc.
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