三维曲边界结构波传播分析的时域谱单元方法

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. 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 was 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 a thin-walled cylindrical structure as an example, the propagation behavior of elastic waves in this structure was calculated by using the curved-edge spectral element method, the straight-edge spectral element method and the classical finite element method, respectively to verify the efficiency and accuracy of the proposed method. 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.