Analysis of a 3-node mixed-shear-projected triangular element method for Reissner-Mindlin plates
Analysis of a 3-node mixed-shear-projected triangular element method for Reissner-Mindlin plates
复制标题
Reissner-Mindlin 板的 3 节点混合剪切投影三角元法分析
DOI：
10.1002/num.22084
复制
发表时间：
2017
影响因子：
3.9
通讯作者：
Xie Xiaoping
中科院分区：
文献类型：
--
作者：
Yu Guozhu;Xie Xiaoping
本文分析了现有的三节点杂交三角形单元MiSP 3，用于Reissner-Mindlin板，该单元在数值基准测试中表现稳健（Ayad，Dhatt，and Batoz，Int J Numer Method Eng 42（1998），1149-1179）。基于Hellinger-Reissner变分原理和MITC族的混合剪切插值/投影技术，MiSP 3单元使用连续分段线性多项式近似位移，使用分段独立平衡模式近似弯矩/剪应力。由于局部消去了弯矩/应力参数，该单元与协调线性三角形位移单元的计算量几乎相同。我们得到了一致的稳定性和收敛结果板的厚度。我们分析的主要工具是力矩/应力近似的自平衡关系、混合剪切插值的性质和剪应力近似的离散Helmholtz分解。© 2016 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 33：241-258，2017
This article analyses an existing 3‐node hybrid triangular element, called MiSP3, for Reissner–Mindlin plates which behaves robustly in numerical benchmark tests (Ayad, Dhatt, and Batoz, Int J Numer Method Eng 42 (1998), 1149–1179). Based on Hellinger‐Reissner variational principle and the mixed shear interpolation/projection technique of MITC family, the MiSP3 element uses continuous piecewise linear polynomials for the approximations of displacements and a piecewise‐independent equilibrium mode for the approximations of bending moments/shear stresses. Due to local elimination of the parameters of moments/stresses, the element is almost of the same computational cost as the conforming linear triangular displacement element. We derive uniform stability and convergence results with respect to the plate thickness. The main tools of our analysis are the self‐equilibrium relation of the moments/stresses approximations, the properties of the mixed shear interpolation and the discrete Helmholtz decomposition of the shear stress approximation. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 241–258, 2017