圆管网格结构的自适应有限元分析方法研究

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。

ADAPTIVE FINITE ELEMENT PROCEDURE FOR PIPE SECTION LATTICED SHELL STRUCTURES

The main objective of the present paper is to judge if the length and shape functions of a beam element in the finite element model of an latticed shell structure are suitable.Firstly the deflection function are derived subject to tension,compression,and pure bending according to the boundary conditions from finite element trial analysis and then the generalized force fields are obtained;Secondly,based on the Zienkiewicz-Zhu error post-processing technique,the generalized force field can be used as the relativly accurate solution,then,the energy norm of the finite element solution and the relative solution are given to determine the raltive error of the beam element.The computation trials proceed after the shape functions and the length of beam elements are adjusted,until the relative error requirement of every beam element in the structure is satisfied.An adaptive static finite element analysis of a single-layer reticulated dome is conducted to illustrate the feasibility and the validity of this method.