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建立了激光惯性导航系统的三维有限元模型,对其力学特性进行了模态分析,建立了整个模型B样条小波有限元模型;研究了一类新的有限元空间,它以B样条小波函数作为有限等参元的形状函数;建立了IMU模型的B样条小波有限元序列,利用B样条小波函数的变尺度特性在不改变网格的剖分下提高分辨率,因此在处理局部应力集中,曲率分布突变边界等应用中具有一定的优势,所以它的结果更接近于实际;最后对系统模型进行了仿真,给出了各个阶次模态值,通过与传统有限元比较发现小波有限元具有收敛性好、求解迅速和网格划分灵活优点,离散的单元数减少了13%,计算时间也是原来的35%,这对于激光惯性导航系统的优化设计具有重要参考价值。
A three-dimensional finite element model of laser inertial navigation system was set up and its mechanical properties were modeled. The finite element model of B-spline wavelet was established. A new finite element space was studied. The B-spline wavelet Function as the finite isoparametric shape function. The B-spline wavelet finite element sequence of the IMU model is established. By using the scale feature of the B-spline wavelet function to improve the resolution without changing the mesh, Stress concentration and sudden change of curvature distribution have some advantages, so its result is closer to reality. Finally, the system model is simulated and the modal values of each order are given. By comparing with the traditional finite element method, it is found that wavelet Finite element has the advantages of good convergence, quick solution and flexible grid division. The number of discrete elements is reduced by 13% and the calculation time is 35%, which is of great value to the optimization design of laser inertial navigation system.