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为了判断杆件结构的有限元分析精度对节点转动刚度是否敏感,并据此调整杆件结构的离散方式,根据Zienkiewicz-Zhu后验误差估计理论,定义了正应力范数来衡量有限元的计算精度,推导了考虑节点刚度的梁单元节点力-位移公式,并以试算得到的梁/杆单元的两节点位移作为边界条件,根据半刚性节点位移-力的公式,给出了杆件需要采用梁单元、杆单元、梁+弹簧单元离散的节点刚度范围,然后通过试算确定杆件结构的合理离散方式。在ANSYS中用APDL语言实现以上算法,并以2个简单结构为例说明了该算法的流程并验证了它的正确性。
In order to judge whether the finite element analysis accuracy of the bar structure is sensitive to the rotation stiffness of the joint and adjust the discretization mode of the bar structure according to the posterior error estimation theory of Zienkiewicz-Zhu, the normal stress norm is defined to measure the finite element calculation The formulas of force and displacement of beam element considering the stiffness of node are deduced. Based on the formula of displacement and force of semi-rigid node, the displacement of two elements of beam / Adopting the discrete stiffness range of beam element, rod element and beam + spring element, the reasonable discrete method of the rod structure is determined through trial calculation. In the ANSYS using APDL language to achieve the above algorithm, and two simple structure as an example to illustrate the flow of the algorithm and verify its correctness.