三维曲边界结构波传播分析的时域谱单元方法

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (20) : 325-333.

论文

三维曲边界结构波传播分析的时域谱单元方法

悦茂苓1，鱼则行1，2，孙佳颖1，徐超1，3

作者信息 +

A time-domain spectral element method for wave propagation analysis of three-dimensional curved-edge structures

YUE Maoling1, YU Zexing1, 2, SUN Jiaying1, XU Chao1, 3

Author information +

文章历史 +

摘要

航空航天工程中存在大量具有复杂曲线或曲面边界的结构，采用弹性波对这类结构进行损伤检测时，分析弹性波在结构中的传播行为是其中的重要环节。目前，数值模拟是研究结构中弹性波传播行为的有效手段。现有的数值仿真方法在对曲边界结构进行建模时多采用直边单元，在结构边界处存在较大的几何近似误差，从而影响了弹性波传播仿真的精度。针对这一问题，本文在时域谱单元方法体系下，推导了一种亚参数27节点曲边谱单元，该单元采用二次插值函数描述单元边界，可以更为准确地描述复杂曲边结构的几何特征，适用于模拟弹性波在此类结构中的传播行为。以薄壁圆筒结构中的波传播问题为例，分别采用曲边谱单元法、直边谱单元法和经典有限元法计算了弹性波在该结构中的传播行为，以验证所提出方法的效率和精度。结果表明：在相同的计算精度下，曲边谱单元法的计算规模远小于有限元法，验证了曲边谱单元法的高效性；在相同的网格规模下，相较于直边谱单元法，曲边谱单元法的计算模型能更好的近似实际结构，从而达到更高的求解精度，并且曲边谱单元法对单元尺寸的变化不敏感，能够以较小的网格规模快速收敛到精确的解。此外，结构的曲率越大，曲边谱单元法相对于直边谱单元法的计算优势越显著。

Abstract

In aerospace engineering, there are a large number of structures with curved edges or curved surfaces, and when elastic waves are used to detect the damage of such structures, the analysis of elastic wave propagation behavior in the structure is an important link, and at present, numerical simulation is an effective method to study the propagation behavior of elastic waves in structures. The existing numerical simulation methods mostly use straight-edge elements when modeling curved-edge structures, and there are large geometric approximation errors at the structural boundaries, which affects the accuracy of elastic wave propagation simulation. To solve this problem, under the time-domain spectral element methodology, a sub-parametric curved-edge spectral element with 27 nodes is derived in this paper, which uses a quadratic interpolation function to describe the element boundary. This element can accurately describe the geometric characteristics of complex curved-edge structures, so it is suitable for simulating the propagation behavior of elastic waves in such structures. Taking the wave propagation problem in thin-walled cylindrical structure as an example, the propagation behavior of elastic waves in this structure is calculated by using the curved-edge spectral element method, straight-edge spectral element method and classical finite element method respectively to verify the efficiency and accuracy of the proposed method. The results show that under the same calculation accuracy, the calculation scale of the curved-edge element method is much smaller than that of the classical finite element method, which verifies the efficiency of the curved-edge element method. Under the same mesh scale, compared with the straight-edge spectral element method, the calculation model of the curved-edge spectral element method can better approximate the actual structure, so as to achieve higher solution accuracy, and the curved edge spectral element method is not sensitive to the change of element size, and can quickly converge to an accurate solution at a smaller mesh scale. In addition, the larger the curvature of the structure, the more significant the computation advantages of the curved-edge element method compared with the straight-edge spectral element method.

导出引用

悦茂苓1, 鱼则行1, 2, 孙佳颖1, 徐超1, 3. 三维曲边界结构波传播分析的时域谱单元方法[J]. 振动与冲击, 2024, 43(20): 325-333

YUE Maoling1, YU Zexing1, 2, SUN Jiaying1, XU Chao1, 3. A time-domain spectral element method for wave propagation analysis of three-dimensional curved-edge structures[J]. Journal of Vibration and Shock, 2024, 43(20): 325-333

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