This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise $H^1$ and $L^2$ norm are also derived. A working procedure to find an approximation for the discrete solution using Newtons method is discussed. Numerical results that justify theoretical estimates are presented.

翻译：本文分析了非协调莫利型虚元方法，用于逼近描述极薄弹性板弯曲的冯·卡门方程的正则解。讨论了非线性问题离散解的局部存在性与唯一性。在精确解的最小正则性假设下，建立了能量范数下的先验误差估计。还推导了分片$H^1$和$L^2$范数下的误差估计。讨论了利用牛顿法求离散解近似值的工作流程。给出了验证理论估计的数值结果。