An effective sub-domain smoothed Galerkin method for free and forced vibration analysis
An effective sub-domain smoothed Galerkin method for free and forced vibration analysis
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DOI：
10.1007/s11012-014-0088-6
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发表时间：
2015-05
期刊：
影响因子：
2.7
通讯作者：
Yigang Wang;D. Hu;Gang Yang;Xu Han;Yuantong T. Gu
中科院分区：
文献类型：
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作者：
Yigang Wang;D. Hu;Gang Yang;Xu Han;Yuantong T. Gu
自由振动和受迫振动分析在结构力学和工程中具有重要意义。开发了子域平滑伽辽金方法，用于二维固体的自由振动和受迫振动分析。该方法综合了无网格伽辽金法和有限元法（FEM）的优点。任意形状的子域是在由无网格节点表示的问题域中预定义的。在每个子域中，基于无网格伽辽金弱公式，通过移动克里金插值可以得到局部离散方程，类似于有限元中高阶单元的离散方程。通过将子域划分为多个平滑单元，应变平滑技术随后可以应用于子域的节点积分。此外，还可以通过基于子域的内部节点传递方程到边界节点方程，将自由度凝聚引入离散方程。该方法的全局动力学方程是基于有限元格式，通过组装子域的所有局部离散方程得到的，并使用标准隐式纽马克时间积分格式进行求解。数值算例证明，子域平滑伽辽金法是一种鲁棒的弹性动力学问题模拟技术，具有计算效率高、精度好的特点。
Free and forced vibration analysis is significant in structural mechanics and engineering. A sub-domain smoothed Galerkin method is developed for free and forced vibration analyses of 2D solids. This method integrates the advantages of mesh-free Galerkin method and finite element method (FEM). The arbitrarily shaped sub-domains are predefined in the problems domain represented by mesh-free nodes. In each sub-domain, based on mesh-free Galerkin weak formulation, the local discrete equation can be obtained by using moving kriging interpolation, which is similar to the discrete equation of a high-order element in FEM. The strain smoothing technique can be subsequently applied to the nodal integration of sub-domain by dividing the sub-domain into several smoothing cells. Moreover, condensation of degrees of freedom can also be introduced into discrete equations by transfer equations of inner nodes to equations of boundary nodes based on sub-domains. The global dynamic equations of the present method are obtained based on the scheme of FEM by assembling all local discrete equations of sub-domains and are solved by using the standard implicit Newmark’s time integration scheme. Numerical examples proved that the sub-domain smoothed Galerkin method is a robust technique to simulation the elastic dynamic problems, which has high computational efficiency and good accuracy.