四边形八节点共旋法平面单元的几何非线性分析

GEOMETRICALLY NONLINEAR ANALYSIS USING A QUADRILATERAL 8-NODE CO-ROTATIONAL PLANE ELEMENT

不同于大部分共旋法研究中所选取的局部坐标系原点及采用的几何一致性原则,该文通过改变局部坐标系原点位置,基于场一致性原则,采用共旋坐标法导出了四边形八节点平面单元在大转动、小应变条件下的几何非线性单元切线刚度矩阵,该单元刚度矩阵虽然不对称,但计算量能明显减少,这在非线性计算中对于减小由于计算机位数限制带来的累积舍入误差和提高迭代的收敛性都有重要意义,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,利用程序对承受端部集中荷载和全梁均布荷载的悬臂梁进行了计算,结果与参考解吻合良好;对拱顶承受竖向集中载荷的坦拱进行了全过程分析,计算结果表明单元具有很好的精度和稳定性,具有一定的实用价值,值得推荐。

A new geometric nonlinear element tangent stiffness matrix for the quadrilateral 8-node plane element under a large rotation with small strain is presented by changing the origin of the coordinate system and adopting a field consistency principle,which is different from other existing co-rotational approach adopting the origin of a local coordinate system and a geometric consistency principle.The stiffness matrix is asymmetric.However,it requires less computation and positively meaningful in reducing the accumulated round-off errors and increasing the convergence of iterations.A Fortran-based nonlinear finite element iteration procedure is established by the Newton-Raphson technique.Two examples including a cantilever beam with a concentrated load and a distributed load and a shallow arch under a concentrated load at arch crown are solved to verify the reliability and computational efficiency of the proposed element formulation.