动态冯·卡门方程的无条件稳定且能量守恒的离散化
Unconditionally stable and energy conserving discretization of the dynamic von Kármán equations
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中文总结 AI 辅助
本文提出一种动态冯·卡门方程的全离散方法，结合非协调Morley有限元与改进型Newmark格式，通过理论分析和数值实验验证了该方法的稳定性、收敛性与误差界。
中文摘要 AI 辅助
本文对动态冯·卡门方程进行全离散近似，空间离散采用非协调Morley有限元方法，时间离散采用能量守恒的改进型无条件稳定Newmark二阶时间步长格式。利用Brouwer不动点定理证明了全离散格式解的存在性，小载荷条件下进一步得到解的唯一性与稳定性估计。针对该全离散格式，推导了分片能量范数下的最优阶先验误差估计，时间方向具有二次收敛性。数值实验结果验证了理论误差界的正确性。
英文摘要
A fully discrete approximation of the dynamic von Kármán equations combines nonconforming Morley finite element methods for spatial discretization with an energy conserving modified unconditionally stable Newmark second- order time-stepping scheme. Brouwer's fixed-point theorem establishes existence of a solution to the fully discrete scheme and further uniqueness and stability estimates follow for small loads. Optimal order a priori error estimates in the piecewise energy norm with quadratic convergence in time are derived for the fully discrete scheme. The results of the numerical experiments validate the theoretical error bounds.
