境界要素法における数値積分誤差

概要

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Errors included in solutions obtained by the boundary element method analysis are generally larger than those by the finite element method analysis in the case that the number of discreted elements is small. One of the reasons is supposed to be attributed to the error which will be produced in the numerical integration of the r,^l_xr,^m_y/r^n type of singular functions in two dimensional elastic problem. In this report the distance r between an observed point and a boundary element was represented graphically by two parameters. Then many functions composing the fundamental solutions could be classified into seven groups and their tendencies along an element were characterized. The following results were obtained: (1) Errors of the numerical integration of the functions are small in the region r_d/L>0.5 even if four points are chosen in gaussian quadrature formulas. (2) The larger the exponent values i, j, k, l, the more increase the errors in the integration of the functions r,^l_xr,^m_y/r^n. Then, the methods to reduce computing time and to decrease errors of the numerical integrations are proposed.
一般社団法人日本機械学会の論文
1986-04-25