基于时域自适应精细算法的插值型无单元Galerkin法及其在弹性动力学中的应用

An Interpolating Element Free Galerkin Method Based on Self-adaptive Precise Algorithm in Time Domain and Its Application in Elastodynamics

将插值型无单元Galerkin法与时域自适应精细算法相结合,提出一种求解弹性动力学问题的方法。通过时域分段展开,将时空耦合的初边值问题转换为一系列的空间边值问题,进而采用加权残值法推导递推形式的插值型无单元Galerkin法求解方程。该方法不仅能方便地直接施加本质边界条件,并且可以避免时间步长较大造成的精度损失。数值算例给出的结果验证了该方法的有效性。

Combining the interpolating element free Galerkin(IEFG)method and the self-adaptive precise algorithm in time domain,a novel algorithm is proposed for structural dynamic analysis in this paper.By expanding variables in each discretized time interval,the coupled spatial and temporal problem is transformed into a series of spatial problems,which are recursively solved by the IEFG method.The corresponding discretized governing equations for structural dynamic analysis are derived using the weighted residual technique.The proposed method can directly impose the essential boundary conditions directly and avoid possible loss of precision resulting from large time steps.The computational results shown in the numerical examples are satisfactory,which can demonstrate the effectiveness of the proposed method.