基于二维线弹性带孔板的虚拟元方法

A Virtual Element Method Based on 2D Linear Elastic Plate with Hole

摘要: 本文应用虚拟元方法研究二维线弹性带孔板问题，该方法的应用克服了线弹性方程数值格式的强制性、数值解的闭锁性以及应力张量的对称性等困难，即不需要显式构造基函数，仅通过单元内部及边界的自由度来构造虚拟元函数空间，进而求出数值解，并给出了半离散和全离散格式的误差估计。通过二维带有圆孔的无限大板线弹性方程的数值计算，证明了理论分析结果的正确性，且相比于传统的有限元法，该方法在解的精确性和收敛性方面具有显著优势。

Abstract: In this paper, the virtual element method is used to study the two-dimensional linear elastic plate with hole problem, the application of this method overcomes the difficulties such as the compulsion of linear elastic equation’s numerical scheme, the locking of numerical solution, and the symmetry of stress tensor, which is no need to explicitly construct the basis function, only through unit interi-or and boundary of freedom to construct the virtual function space, then calculate the numerical solution. The error estimates for semi-discrete and fully discrete schemes are given. Through the numerical calculation of linear elastic equation of two-dimensional infinite plate with circular holes, the correctness of the theoretical analysis result is proved. Compared with traditional finite element method, this method has significant advantages in solution’s accuracy and convergence.