线弹性力学的无锁面心有限体积（FCFV）方法
A locking-free face-centred finite volume (FCFV) method for linear elasticity
摘要：
提出了一种求解线弹性力学方程的面心有限体积（FCFV）方法。FCFV是一个混合的混合配方，具有系统的一阶方程，它定义了网格元素的面（在两个维度的边缘）上的未知数。应力张量的对称性是强有力的强制使用著名的Voigt符号和每个单元内的位移和应力场得到的明确的公式通过元素。所得到的FCFV方法是强大的和锁定的几乎不可压缩的限制。在二维和三维的数值实验表明，最佳的收敛的位移和应力场没有任何重建。此外，FCFV方法的精度对网格变形和拉伸不敏感。经典的基准测试，包括Kirch的板和库克的膜问题，在二维以及三维问题，涉及剪切现象，加压薄壳和复杂的几何形状，提出了显示所提出的方法的能力和潜力。
英文摘要：
A face-centred finite volume (FCFV) method is proposed for the linear elasticity equation. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the unknowns on the faces (edges in two dimensions) of the mesh elements. The symmetry of the stress tensor is strongly enforced using the well-known Voigt notation and the displacement and stress fields inside each cell are obtained element-wise by means of explicit formulas. The resulting FCFV method is robust and locking-free in the nearly incompressible limit. Numerical experiments in two and three dimensions show optimal convergence of the displacement and the stress fields without any reconstruction. Moreover, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. Classical benchmark tests including Kirch's plate and Cook's membrane problems in two dimensions as well as three dimensional problems involving shear phenomenons, pressurised thin shells and complex geometries are presented to show the capability and potential of the proposed methodology.
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