高效双非线性平面梁单元算法研究

Research on efficient coupling nonlinear algorithm for plane beam element

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 simple and efficient plane beam element for structural geometrical and material nonlinear analysis is proposed based on co-rotational procedure and field consistency, and corresponding computer program is also developed. Material nonlinear effect is considered in co-rotational coordinate system. Fiber integration method is used to cope with arbitrary section of plane beam element and to derive the section tangent stiffness matrix, and element tangent stiffness matrix is acquired by using the principle of virtual work. Iteration is not needed during this process, which makes computational efficiency can be remarkably improved. Geometrical nonlinear effect is considered by variables are transformed from co-rotational coordinate system to global coordinate system. With the developed method, numerical results of an elbow frame structure exhibit good agreement with the experimental data in a geometrically nonlinear analysis. Considering the material nonlinearity solely, differences between obtained numerical result of a simply supported beam and analytical solution and result available in reference are 4.2% and 1.5%, respectively. When both geometrical and material nonlinearities are taken into account together, results by the developed method deviate those from reference and ANSYS are 2.9% and 5.9%, respectively. Additionally, the curve of loading versus displacement is more relatively close to the practical case.