论文部分内容阅读
为了判断网格结构有限元模型中梁单元的长度和插值函数是否合理并对此进行调整,首先推导了梁在受拉、受压、纯弯3种情况下的挠曲微分方程,以有限元试算得到的梁单元两端节点力为边界条件,求出了梁单元广义力分布场的解析解;然后,根据Zienkiewicz-Zhu后验误差估计理论,以该解析解为广义力相对精确解,推导了广义力有限元解和广义力相对精确解的能量范数以确定梁单元的相对误差。在试算过程中,如果网格结构中每个梁单元的相对误差都满足精度要求,则终止试算过程,否则调整梁单元的插值函数或长度后再进行试算。以单层球面网壳的自适应有限元静力分析为例验证了该方法的正确性和可行性。
In order to judge whether the length and interpolation function of the beam element in the finite element model of the grid structure are reasonable or not, the deflection differential equations of the beam under tension, compression and pure bending are deduced firstly. The finite element method Based on the posterior error estimation theory of Zienkiewicz-Zhu, the analytic solution is regarded as the relative exact solution of generalized force, The energy norm of generalized force finite element solution and relative exact solution of generalized force are deduced to determine the relative error of beam element. During the trial calculation, if the relative error of each beam element in the grid structure meets the accuracy requirements, the trial calculation process is terminated. Otherwise, the interpolation function or length of the beam element is adjusted before performing the trial calculation. The static and dynamic finite element analysis of a single-layer spherical reticulated shell is used to verify the correctness and feasibility of the method.