矩形底面扁球面网壳的分岔问题

Bifurcation Problem of Shallow Reticulated Spherical Shells with Rectangular Bottom

对曲面为正三角形网格矩形底面扁球面单层网壳,用拟壳法建立非线性动力学方程,在固定夹紧的边界条件下,给出满足边界条件的动态解。通过Galerkin法得到该问题的非线性动力学方程,用Floquent指数方法研究系统的分岔问题,讨论了平衡点(奇点)领域的稳定性问题。并且通过数字仿真绘出了不同平衡点处系统的分岔图,指出系统在动静载荷作用下平衡位置的变化情况。

The nonlinear dynamic equations for reticulated shallow spherical single-layer shells with equi-lateral triangular lattices and rectangular bottom were established by using the method of quasi-shells, and the dynamic solution fulfilling the boundary conditions was given under the clamped conditions.The nonlinear dynamic equations for this problem were obtained by using Galerkin method.The problem of statistic at the equilibrium point of the system was discussed by exponent Floquet.Lastly the bifurcation map of the equilibrium point was plotted by numerical emulation under the differentstate.The movement of the equilibrium point of the sysem under the load of both dynamic and static was indicated.