基于面积坐标和解析试函数的薄板元

Thin plate element based on area coordinate and analytical trial functions

为体现离散法与解析法的互补和渗透,构造基于第二类四边形面积坐标的广义协调薄板元AATF-BQ4;根据薄板理论的控制方程,采用Kirchhoff直法线假设求解基本解析解,并作为试函数构造单元AATF-BQ4.数值算例表明,单元AATF-BQ4具有较高的精度和较好的稳定性,适用于实际工程计算应用.

To embody the complementary and penetration between discrete method and analytical method, a generalized conforming thin plate element called AATF-BQ4 is constructed on the basis of the second type of quadrilateral area coordinate ; according to the governing equations of thin plate theory, the fundamental analytical solutions are obtained using Kirchhoff straight normal line assumption and it is taken as the trial functions to construct the element AATF-BQ4. The numerical examples show that the element AATF-BQ4 is with higher precision and better stability, which is suitable for the actual engineering application.