【摘要】 本文利用边界型最小二乘配点法,取极座标下的双调和方程的特解序列作为试函数,对开大孔的薄板弯曲问题进行了计算研究。计算中应用了复变函数保角变换的技术,得到了具有正多边形孔的圆板弯曲问题的近似解。这种方法可推广至其它形状的孔与其它形状的外边界。此外,在计算过程中提出了试函数逐项加权的方法,在一定程度上改善了矩阵病态的情况。更多还原

【Abstract】 In this paper,the least square boundary collocation method is used to analyzethe problem for the bending of thin plates with holes.The trial functions areformed by the series of particular solutions of the biharmonic equations in thepolar coordinate system.The solution for the bendsng problem of circular plateswith regular polygon holes has been achieved by using the conformal transforma-tion technique of the function of complex variables.This method can be extendedto the solution of the bending problm of plates with holes or outer configurationswhich have other shapes.In addition,the series of item by item weighting methodhas been employed in the calculating process,and has improved the ill conditionof the matrix to a certain extent.更多还原