高效双非线性平面梁单元算法研究

发布时间：2018-11-14 14:40

【摘要】：基于随转坐标法和场一致性原则发展了一种用于结构几何与材料双非线性分析的平面梁单元算法,并编制了相应的计算机程序。在随转坐标系下计入材料非线性,采用截面纤维积分法处理任意形状的平面梁单元截面并导出截面切线刚度矩阵,并利用虚功原理得到单元切线刚度矩阵,此过程无需迭代,因而使计算效率得到很大提高;几何非线性效应则通过变量在随转坐标系与结构坐标系之间的转换得以体现。用本文方法对肘式框架的几何非线性进行分析,计算结果与试验结果吻合良好;对简支梁进行分析,在只考虑材料非线性而不考虑几何非线性情况下,本文结果和已有文献结果与解析解的误差分别为1.5%和4.2%;在考虑几何与材料双非线性情况下,本文结果和已有文献结果与ANSYS程序解的误差分别为2.9%和5.9%,与已有文献结果相比,本文所得受力后期的荷载-位移曲线更接近实际情况。
[Abstract]:Based on the coordinate with rotation method and the principle of field consistency, a plane beam element algorithm for the double nonlinear analysis of structure geometry and material is developed, and the corresponding computer program is compiled. Considering the material nonlinearity in the rotating coordinate system, the section fiber integral method is used to deal with the section of the plane beam element with arbitrary shape and the tangent stiffness matrix of the section is derived, and the tangent stiffness matrix of the element is obtained by using the virtual work principle. Therefore, the computational efficiency is greatly improved. The geometric nonlinear effect is reflected by the transformation of variables between the rotated coordinate system and the structural coordinate system. The geometric nonlinearity of elbow frame is analyzed by using the method in this paper. The calculated results are in good agreement with the experimental results. Based on the analysis of simply supported beams, the errors of the results obtained in this paper and the analytical solutions are 1.5% and 4.2%, respectively, when only the material nonlinearity is considered, but not the geometric nonlinearity. In the case of both geometric and material nonlinearity, the errors between the results obtained in this paper and the results obtained in previous literatures are 2.9% and 5.9%, respectively, compared with the results obtained in the previous literatures. The load-displacement curve obtained in this paper is closer to the actual situation.
【作者单位】：长沙理工大学土木与建筑工程学院;广州大学工程抗震研究中心;
【基金】：国家重点基础研究发展计划项目(2011CB013606) 中国博士后基金项目(2014M562154) 湖南省教育厅青年基金项目(14B008) 长沙理工大学土木工程重点学科基金项目(13ZDXK02)
【分类号】：TU311

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