基于曲边平面谱单元的弹性波传播分析

针对现有的谱单元多将单元几何边界考虑为直线或平面,对具有复杂曲线或曲面形状的结构几何离散近似误差较大,从而影响了弹性波传播分析精度的问题,推导了一种亚参数曲边平面谱单元,对单元几何形状采用二次插值,对位移场函数可采用高于二阶的任意阶插值,并讨论了一般高次曲边/曲面谱单元的推导方法. 以矩形平面结构中的波传播分析为例,对比了曲边谱单元、直边谱单元及常规有限元的数值模拟结果,验证了单元的有效性. 以具有曲线边界的圆环结构中的波传播分析为例,对比了采用曲边和直边谱单元数值模拟结果的差异. 结果表明,采用直边单元近似曲边结构,由于几何误差较大,弹性波传播分析结果误差较大;曲边单元能够获得更好的模拟精度. 

Elastic Wave Propagation Analysis Using a Curved Two-Dimensional Spectral Element

Element boundaries were treated as straight or plane in common spectral element, resulting in large errors in geometry approximation of structures with curve boundaries. In this paper, a sub-parametric plane spectral element was developed with a quadratic function for element shape interpolation. Any higher order than two functions can be used to interpolate element displacements field. The general procedure on establishment of a high order curved spectral element was discussed. A numerical example of elastic wave propagation in a rectangular plane structure was used to verify the proposed element. The analysis results were compared with the results given by straight spectral elements and classic finite elements. Then elastic wave propagation in a ring structure was analyzed by the proposed element and the common straight edge spectral element. The results show that there is larger discretion error using straight-edge element than curved-edge element for geometry approximation of complex structures with curve boundaries. Using the proposed curved-edge element in structural wave propagation will give better accuracy.