A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells
A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells
复制标题
DOI：
10.1002/nme.3000
复制
发表时间：
2011-02
影响因子：
2.9
通讯作者：
X. Cui;Guirong Liu;Guangyao Li;Guiyong Zhang
中科院分区：
文献类型：
--
作者：
X. Cui;Guirong Liu;Guangyao Li;Guiyong Zhang
利用广义梯度光滑化技术和径向点插值法，提出了只以挠度为节点变量的薄板计算公式。挠度场用RPIM形函数近似，形函数具有Kronecker Delta性质，便于施加本质边界条件。基于背景的三节点三角形单元构造了三类同时作为数值积分区域的光滑域，并对每一类光滑域进行广义梯度光顺运算，得到光滑曲率。然后利用广义光滑Galerkin弱形式建立离散的系统方程。在构造曲率场的过程中施加了旋转的本质边界条件，并像标准有限元一样施加了平移边界条件。用该方法对多个算例进行了静力和自由振动分析，并将计算结果与解析结果和文献中的结果进行了比较。结果表明，即使对于非常不规则的背景单元，该公式也能得到非常稳定和准确的解。版权所有©2010 John Wiley&Sons，Ltd.
A formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method (RPIM). The deflection fields are approximated using the RPIM shape functions which possess the Kronecker Delta property for easy impositions of essential boundary conditions. Three types of smoothing domains, which are also serving as the numerical integrations domains, are constructed based on the background three‐node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential boundary conditions of rotations are imposed in the process of constructing the curvature field, and the translation boundary conditions are imposed as in the standard FEM. A number of numerical examples, including both static and free vibration analysis, are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures. The results show that the present formulation can obtain very stable and accurate solutions, even for the extremely irregular background cells. Copyright © 2010 John Wiley & Sons, Ltd.