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本文用加权残数法分析薄板弯曲问题。选正弦级数与多项式和样条梁函数为矩形薄板的试函数(位移函数),ω=CXY,使梁函数X、Y变量分离,用双重幂级数做试函数分析平行四边形薄板,并推导平行四边形板的斜坐标系偏微分方程及其边界条件,经通过最小二乘法的直接法及最小二乘配点法对几种边界条件做计算,证明所选试函数的待定参数最少,具有较好的收敛性,精度较高。
This paper uses the weighted residual method to analyze the bending problem of thin plates. Select sine series and polynomial and spline beam function as the trial function (displacement function) of the rectangular thin plate, ω=CXY, separate the X and Y variables of the beam function, use the double power series as the trial function to analyze the parallelogram thin plate, and derive The parallelogram quadratic plate partial differential equations and their boundary conditions are calculated by the least squares direct method and the least squares collocation method for several kinds of boundary conditions. It is proved that the undetermined parameters of the selected trial function is the least, and it is better Convergence, high precision.