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Automatic derivation of positively conditions inside boundary elements with the help of the REDOG computer logic percale

机译:借助REDOG计算机逻辑功能自动得出边界元素内部的正条件

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The very well-known shape functions are used in classical boundary element analysis for the constructor of the polynomial interpolation function p for the approximation to the unknown field quantity u. In this note, we show the usefulness of the recent REDLOG Reduce computer logic package of Dolzmann and Strurm for the constructor of positively and analogous parametric feasibility conditions, based on the nodal values of the polynomial p, inside the whole boundary element. A simple one-dimensional case, based on the cassia quadratic element, and a more difficult two-dimensional case, based on a quadratic triangular element, are used for the illustration of the approach, whereas several related conclusions are also drawn. The present results are applicable to cases where the positively or the negativity or just the boundedness of the unknown quantity is required (such as the case of he pressure distribution in contact problems and the opening displacement in crack problems) and significantly extend the already available recent related computational quantifier elimination research results.
机译:在经典的边界元素分析中,众所周知的形状函数用于多项式插值函数p的构造函数,以逼近未知场量u。在本说明中,我们基于整个边界元素内多项式p的节点值,展示了Dolzmann和Strurm的最新REDLOG Reduce计算机逻辑软件包对正和类似参数可行条件的构造函数的有用性。一种简单的基于决明子二次元的情况,以及一个较困难的基于二次三角元的二维情况,用于说明该方法,同时还得出了一些相关的结论。本结果适用于需要正数或负数或仅需要未知量的有界数的情况(例如接触问题中的压力分布和裂纹问题中的开口位移的情况),并且极大地扩展了最近已经可用的情况。相关的计算量词消除研究成果。

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