基于ANSYS二次开发的几何非线性平面梁单元

A geometric nonlinear plane beam element based on secondary development of ANSYS

共旋坐标法(C.R法)具有在局部坐标系考虑材料非线性,通过局部坐标系与结构坐标系之间内力和切线刚度矩阵的转换矩阵来考虑几何非线性,从而实现两种非线性脱耦的优点,C.R法相对于其它非线性有限元列式而言较少运用于商业程序。本文利用ANSYS平台提供的单元二次开发工具——用户可编程特性(UPFs),开发了基于C.R法的几何非线性平面梁单元,给出了详细的算法及流程,通过多个算例对本文算法及程序进行了验证。研究表明:该方法能有效利用共旋法非线性单元和ANSYS商业程序的优点,对于方框架在对边中点受一对集中力的算例1,采用二次开发的用户梁单元与beam3梁单元在每个荷载步下收敛所需的迭代次数分别为3次和6次;对于预应力钢筋混凝土悬臂梁发生大变形的算例2,上述两种单元模型进行非线性计算能收敛的预应力加载系数分别为132和128,可知本文基于共旋法得到的ANSYS二次开发用户梁单元提高了非线性计算的效率和能力,可用于平面梁结构的几何非线性分析。

Through the use of co-rotational coordinate method(CR method),the material non-linearity is captured in the local coordinate system,whereas the geometric non-linearity induced by large displacement,is incorporated in the transformation matrices relating local and global internal force vectors and tangent stiffness matrices,thus two kinds of nonlinearities are successfully decoupled.CR method is less used in commercial programs than other nonlinear finite element methods.In this paper,a geometric nonlinear planar beam element based on co-rotational method is developed by using UPFs,a unit secondary development tool provided by ANSYS platform.The algorithm and program are verified by several examples,and the detailed algorithm and procedure are obtained.The results show that this method can effectively utilize the advantages of the co-rotational nonlinear element and ANSYS commercial program.For example-1 of a square frame subjected to a concentrated force at the corner,iteration times applying secondary development user beam element and beam 3 element to get convergence are 3 and 6 respectively;for example-2 of a prestressed reinforced concrete cantilever beam under large deformation,the convergent prestressing loading factors calculated with nonlinear method of the above two elements are respectively 132 and 128.It is obtained that the ANSYS secondary development user beam element based on co-rotational coordinate method improves the efficiency and capability of nonlinear calculation,and the present method is applicable to the geometrically nonlinear analysis of planar beam structures.