混合边界粒子法在分析平板弯曲问题中的应用

A Mixed Boundary Partical Method for Analyzing Bending Problem of Plates

本文提出一种平板弯曲问题的数值方法—混合边界粒子法。该方法无需事先进行形状函数假设,直接从平板弯曲问题的基本微分方程出发,通过在局部区域内将微分方程转化为积分方程并利用数值积分,得到指定点的离散解。通过选择合理的指定点途径,最终使得任意指定点的数值可以用边界点上的未知量表达,从而大幅度减少了未知量的个数和系数的计算时间。通过数值分析并将结果与参考文献的结果进行比较,验证了本方法的有效性和精确性。

A mixed boundary partical method was proposed for analyzing the bending problem of plates.No prior assumption of the shape of deflection was employed.The fundamental differential equations were established.By transforming these differential equations into integral equations in a small area and using numerical integration,the discrete solution of the appointed point was obtained.By choosing the appointed point according to a regular order,the quantities of any point were expressed by the unknown quantities of the boundary points and the computer time of the coefficient can be reduced greatly.The numerical calculation was carried out.By comparing the numerical results with those previously published,the efficiency and accuracy of the present method were investigated.