可带铰空间梁单元几何非线性分析的随转坐标法  

Co-rotational coordinate method for geometric nonlinear analysis of 3-D beam element with/without hinge

作　　者：邓继华[1,2] 邵旭东[1] 彭建新[2] 

机构地区：[1]湖南大学土木工程学院,长沙410082 [2]长沙理工大学土木与建筑学院,长沙410076

出　　处：《应用力学学报》2013年第4期630-634,653-654,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51008037)

摘　　要：为了降低可带铰空间梁单元切线刚度矩阵的运算量、提高非线性计算精度,本文首先通过建立单元随转坐标系得到扣除刚体位移后结构变形与总位移之间的关系,进而基于场一致性原则导出空间梁单元的几何非线性单元切线刚度矩阵,并在此基础上根据带铰梁端弯矩为零的受力特征得到考虑梁端带铰的单元切线刚度矩阵表达式。该方法利用随转坐标系下除单元轴向相对位移外的其余五个线位移均为零的特点,降低了计算单元切线刚度矩阵所需的相关矩阵阶次,因此减少了运算量。对对角点受拉铰接的方棱形框架进行计算,得出本文结果与解析解的最大误差为0.226%;对45°弯梁和带铰平面结构的空间受力进行计算,得出前者与已有文献提供的解非常接近,误差为0.027%～2.394%,后者与ANSYS计算结果的最大误差为1.082%,表明本文算法具有良好的精度。In order to decrease calculation amount of geometric nonlinear analysis and increase calculation accuracy of the 3-D beam element with/without hinge,the relation between structural deformation excluding rigid displacement and total displacement is firstly obtained from constructing co-rotational coordinate system.According to the law of consistency of field,tangential stiffness matrix of geometric nonlinear analysis is developed for 3-D beam element.The mechanical characteristics of zero bending moment at beam ends with hinge are applied,and then tangential stiffness matrix of geometric nonlinear analysis for 3-D beam element with/without hinge is obtained.Because that the displacements for five directions are 0 except that axial displacement under co-rotational coordinate system,the dependent matrix order can be decreased for computing tangential stiffness matrix and thus decrease calculation amount.A corner-pulled square prism rigid frame is analyzed and the maximum error is 0.226% compared with analytical results.Moreover,a curved beam with an angle of 45°and plane structures are respectively computed.For the curved beam the results are in good agreement with those provided by available literature,error is from 0.027% to 2.394%.For plane structure,the maximum error is 1.082% as compared with that obtained from ANSYS software.This shows that the method developed possesses good accuracy.

关 键 词：空间梁元 铰 几何非线性 切线刚度矩阵 随转坐标法 

分 类 号：TU323[建筑科学—结构工程]