基于面积坐标和解析试函数的厚薄通用板单元

Two thick/thin plate elements based on the area coordinate and analytical trial functions

求出了Mindlin-Reissner厚板理论控制方程的基本解析解,以其作为试探函数构造了两个基于第二类四边形面积坐标的广义协调厚薄通用板单元AATF-PQ4a和AATF-PQ4b;在此基础上计算了承受均布荷载方板的中心挠度和中心弯矩。结果表明:两种单元随网格加密而趋近于精确解,表现出较高的精度和较好的收敛性,而且AATF-PQ4b的收敛速度比AATF-PQ4a快;对于薄板极限情况,这两种厚薄通用板单元自动退化为薄板单元,完全无剪切闭锁现象发生;两种板单元均对网格畸变不敏感,具有较好的稳定性,适用于实际工程计算。

Two generalized conforming thick/thin plate elements called AATF-PQ4a and AATF-PQ4b are developed based on the quadrilateral area coordinate system. Based on the governing equations of Mindlin-Reissner plate theory, the fundamental analytical solutions are derived firstly, then the fundamental solutions are used as trial functions to formulate element AATF-PQ4a and AATF-PQ4b. For the case of thin plate, this thick/thin plate element can be degraded into corresponding thin plate element automatically and is free from shear locking. Through calculating central deflection and central moment of square plate under uniform loading, results from these two kinds of elements converge to the exact solution with mesh refinement, and the convergentspeed of AATF-PQ4b is faster than that of AATF-PQ4a. The elements possess higher accuracy, better convergence and stronger stability. Moreover, they are not sensitive to mesh distortion, which are suitable for engineering applications.