基于TRUNC板元的样条综合离散法

The Spline Synthetic Discrete Method Based on the TRUNC Triangular Plate Bending Element

本文根据文提出的 TRUNC 元刚度矩阵的推导方法,推出了该元的显式刚度矩阵及内力、内力矩表达式,同时,用 TRUNC 元的有限元法及基于 TRUNC 元的一维样条综合离散法计算了各种支承条件下方板、斜板、菱形板、梯形板及开孔板弯曲的静力问题。并对两种方法进行了比较。结果表明,TRUNC 元结构简单。大多数情况下数值精度高。与样条综合离散法这种精度高、未知量少的数值方法相结合,具有广泛的应用前景。

According to the establishing idea of the stiffness matrics of the TRUNC thin plate bending el ement,the explicit stiffness matrics,the stress and the bending reorient formations of the element are deduced.The static problems of square plate with various supported conditions,rhombic plate, trapezoid plate and plate with opening are analyzied by SSDM and finite element method based on the element,The stiffness matries of the element is simple and the calculating results show that the element is high.accuracy and can improved the accuracy of SSDM when it is used with SSDM which is a new numerical method with smaller number of unknowns than FEM but has almoctly the same accuracy.