样条函数康特诺维奇杂交元法在复合材料板弯曲中的应用

The Application of Kantorovich Hybrid Method to the Plate Bending

本文通过修正余能原理,用三次B 样条函数对应力和位移场进行插值,提出一种新的杂交元,应用离散的康特诺维奇法解决了金属和复合材料的弯曲问题。该法具有收敛快、计算精度高、处理边界条件方便的特点,能得到与位移同一精度的应力解,而且不存在多余零能模式和闭锁问题,是一种解决板弯曲问题的行之有效的计算方法。

Using the cubic B—Spline function as interpolation functions of stress and displacement,thispaper has solved the bending problem of isotropic and anisotropic plate with modified complementenergy principle and newly created kantorovich method.The method has advantages of high preci-sion,rapid convergence and the convenience to deal with various boundary conditions.It has ob-tained stress solution with the same precision of displacement and does not exhibit locking effectand kinematic deformation mode,and is proved to be an effective method in solving bending prob-lems of plate.