大转动平面梁有限元分析的共旋坐标法

虽然大转动平面梁单元已有很多,但其中许多太复杂,缺乏计算效率,值得改进。采用共旋坐标法准确的首次导出了平面梁单元发生大转动小应变时的非对称单元切线刚度矩阵,利用这一非对称的单元切线刚度矩阵由Newton-Raphson迭代法编制了一个FORTRAN程序NPFSAP,并获得了大转动梁、方形和圆形框架的高精度数值解,表明了这种非线性单元列式的正确性和非线性求解过程的收敛性,非对称单元切线刚度矩阵值得推介。

CO-ROTATIONAL PROCEDURE FOR FINITE ELEMENT ANALYSIS OF PLANE BEAM UNDER LARGE ROTATIONAL DISPLACEMENT

Although many plane beam elements of large rotation have been developed, much of these early works were surprisingly sophisticated and worth improvement. Starting from geometric and physical relations of the plane frame, this work successfully applied co-rotational procedure to derive non-linear asymmetric tangent stiffness matrix of plane beam element under large but small-strained rotational displacement. Nonlinear finite element iteration procedure is also established by the Newton-Raphson technique, and a corresponding FORTRAN program NPFSAP completed. Numerical analysis results of high accuracy for beams, square and circular frames of large rotational displacement are thus computed and obtained. Computations indicate that formulations for the nonlinear element are of higher performance and validation, and that the nonlinear solution procedures are of rapid and stable convergence. The method and its program NPFSAP could be helpful for engineering designers to analyze beam and frame structures more accurately.