NURBS-augmented finite element method for stability analysis of arbitrary thin plates
NURBS-augmented finite element method for stability analysis of arbitrary thin plates
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DOI：
10.1007/s00366-018-0603-9
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发表时间：
2019-04
影响因子：
8.7
通讯作者：
B. P. Mishra;M. Barik
中科院分区：
文献类型：
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作者：
B. P. Mishra;M. Barik
在板的分析中，几何形状起着非常重要的作用。在等几何分析中，采用非均匀有理B样条（NURBS）基函数来表示几何变量和场变量。这些基函数能够准确地表示几何形状。它们本质上是非插值的，因此不满足克罗内克-德尔塔性质。因此，很难在控制变量处强制执行本质边界条件。提出了一种新的方法，称为BSBS-增广有限元法（NAFEM）（Mishra和Barik，Comput Struct， https://doi.org/10.1016/j.compstruc.2017.10.011 ，2017）和任意形状的板成功地处理了弯曲分析。在NAFEM中，作者采用有限元基函数作为场变量，因为它们满足Kronecker-Delta性质，因此边界条件易于实施，并且NURBS基函数用于几何形状，从而准确地表示板的形状。在目前的工作中，同样的扩展具有不同的几何形状和边界条件的板的稳定性分析，结果被发现是在良好的协议与现有的。还考虑了一些新的形状，并给出了新的结果。
In the analysis of a plate, the geometry plays a very important role. The non-uniform rational B-spline (NURBS) basis functions are employed for the representation of the geometry and field variables in the isogeometric analysis. These basis functions are able to represent the geometry accurately. They are non-interpolating in nature, and hence do not satisfy the Kronecker-Delta property. Hence, it becomes difficult to enforce the essential boundary conditions at the control variables. A new method called NURBS-augmented finite element method (NAFEM) was proposed (Mishra and Barik, Comput Struct, https://doi.org/10.1016/j.compstruc.2017.10.011 , 2017) and arbitrary shaped plates were successfully dealt for bending analysis. In the NAFEM, the authors adopted the finite element basis functions for the field variables as they satisfy the Kronecker-Delta property so that the boundary conditions were enforced with ease and the NURBS basis functions were employed for the geometry, thereby representing the shape of the plate accurately. In the present work, the same is extended for stability analysis of plates having different geometries and boundary conditions and the results are found to be in excellent agreement with the existing ones. Some new shapes have also been considered, and the new results are presented.