解平行四边形板弯曲问题的GD法

采用GD法分析了平行四边表板的弯曲问题.利用坐标变换将平行四边形板域变换到正方形板域,并将控制方程及其相应的边界条件变换到该正方形域内,运用GD法对新控制方程进行求解.数值计算结果表明,GD法具有数学原理严谨、精度高等优点,是一种求解平行四边形弯曲问题的较好的数值方法.

Solving Bending Problem of Parallelogram Plates by GD Method

This paper uses the coordinate transformation to map the parallelogram plate domain into a square plate domain.The control equations and corresponding boundary conditions are transformed into this square domain.Then,the new control equations are solved by GD（General differential）method.The GD method is a numerical method solving partial differential equations based on Taylor series.By expressing each order derivative of one node as the weighted sum of function values of global nodes,the partial differential equation can be converted to the algebraic equations about the function values of the node.The numerical results show that,GD method has rigorous mathematical principles and higher precision,which is a better numerical method for solving the problem of bending parallelogram.