A meshless method for the nonlinear von K?rm?n plate with multiple folds of complex shape
A meshless method for the nonlinear von K?rm?n plate with multiple folds of complex shape
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复杂形状多重褶皱非线性von K?rm?n板的无网格方法
DOI：
10.1007/s00466-019-01671-w
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发表时间：
2019
影响因子：
4.1
通讯作者：
Bilotti Emiliano
中科院分区：
文献类型：
--
作者：
Barbieri Ettore;Ventura Leonardo;Grignoli Davide;Bilotti Emiliano
提出了一种求解含有褶皱的von Kármán板的非线性方程的无网格离散方法。板具有Mindlin-Reissner运动学，其中转动与法向挠度的导数无关，因此用不同的形函数离散。在裂缝中，位移是不连续的，在褶皱中，旋转是不连续的。为了在旋转中引入不连续性，我们使用了作者先前为裂纹导出的丰富的权函数(Barbieri等人。见Int J Numer方法Eng 90(2)：177-195,2012)。使用这种方法，不需要为折叠引入额外的自由度，网格也不需要遵循折叠线。相反，折叠可以是任意定向的，并且在边界上或在板的内部具有端点。此外，褶皱的几何形状可以是直的，也可以有扭结的。结果表明，对于不同的折叠构型，该方法可以再现折叠线的锐边，并与由参考解得到的屈曲或载荷-位移曲线的解析式进行比较，结果令人满意。
We present a meshless discretisation method for the solution of the non-linear equations of the von Kármán plate containing folds. The plate has Mindlin–Reissner kinematics where the rotations are independent of the derivatives of the normal deflection, hence discretised with different shape functions. While in cracks displacements are discontinuous, in folds, rotations are discontinuous. To introduce a discontinuity in the rotations, we use an enriched weight function previously derived by the authors for cracks (Barbieri et al. in Int J Numer Methods Eng 90(2):177–195, 2012). With this approach, there is no need to introduce additional degrees of freedom for the folds, nor the mesh needs to follow the folding lines. Instead, the folds can be arbitrarily oriented and have endpoints either on the boundary or internal to the plate. Also, the geometry of the folds can be straight or have kinks. The results show that the method can reproduce the sharp edges of the folding lines, for various folding configurations and compare satisfactorily with analytical formulas for buckling or load-displacement curves from reference solutions.