方板弹性突跳的数值模拟──第一部分:理论和计算方案

NUMERICAL SIMULATION OF SNAP-THROUGH OF SQUARE PLATE──PartⅠ:Theory and Numerical Methods

在非线性有限元通用程序中，对叉型分岔问题，本文提出一个搜索分枝方向的方法，该方法不需计算切线刚度矩阵的导数，就能确定所有分枝方向。根据Ｌａｇｒａｎｇｅ－Ｄｉｒｉｃｈｌｅｔ定理判别各平衡状态的稳定性。对四边夹支边界条件下、受面内压力作用的方板在后屈曲过程中的力学行为进行了大范围数值追踪，对各种平衡状态的稳定性进行了判别，其中稳定的平衡解可以模拟方板弹性突跳的整个过程，包括加载过程中的弹性突跳和卸载过程中的弹性突跳。计算结果和前人的实验结果进行了比较。本文第一部分讨论计算方法，给出计算方案；第二部分为方板在后屈曲过程中弹性突跳的计算结果。

To search direction of each solution branch at pitch-fork bifurcation point, a numerical method is proposed. Because this method does not require information of derivatives of tangential stiffness matrix, it is suitable for general nonlinear finite element program. Stability of equilibrium corresponding to each solution curve is judged by Lagrange-Dirichlet theorem. The solution path in post-buckling of a square plate is traced globally and equilibrium stability of the plate was judged. The stable equilibrium can simulate the whole process of snap-through of square plate during loading and unloading. The result agrees with available experimental data. Numerical methods and algorithm are proposed and numerical results of snap-through of square plate are compared with experimental data.