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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。
A planar beam element algorithm for double nonlinear analysis of structure geometry and material was developed based on the principle of random coordinate and field consistency, and a corresponding computer program was developed. The material non-linearity is taken into account in the rotation coordinate system. The cross-section fiber integral method is used to deal with cross-section of planar beam element of arbitrary shape and the tangent stiffness matrix of the section is deduced. The tangent stiffness matrix of element is obtained by virtual work principle. The computational efficiency is greatly improved; the geometric nonlinear effect is reflected by the transformation of the variables between the coordinate system of rotation and the coordinate system of the structure. The geometrical nonlinearity of the elbow frame is analyzed by the method in this paper. The calculated results are in good agreement with the experimental results. When the simply supported beam is analyzed, considering only the material nonlinearity without considering the geometric nonlinearity, The errors between the results and the analytical solutions are 1.5% and 4.2% respectively. The error between the proposed results and the ANSYS programs is 2.9% and 5.9%, respectively, considering the bi-nonlinearity of geometry and material. Compared with the existing literature Compared with the result, the load-displacement curve obtained in this paper is closer to the actual situation.