复合材料层合板结构的非协调扩展逐层方法研究
发布时间：2019-05-20 13:22
【摘要】：复合材料层合板壳是工程中使用非常广泛的结构,因此出现大量关于层合板壳分析理论及损伤分析理论。扩展逐层法结合了逐层法和扩展有限单元法的优势,为复合材料层合结构的损伤研究提供了一种精确的分析方法。但是在实际应用中发现,扩展逐层法分析弯曲模型的收敛速度慢,尤其是在分析大弯曲变形问题时,为了达到一定的精度要求需要划分非常细的网格,因此将耗费大量的计算时间。此外,对于复合材料层合板结构,由于分层和裂纹的出现,弯曲模态时有发生。本文利用Wilson非协调技术在分析弯曲变形时的优势,提高扩展逐层法的收敛速度。将Wilson非协调技术分别引入到扩展有限单元、逐层法和扩展逐层法中,建立了非协调扩展有限单元法(IXFEM)、非协调逐层法(ILWM)和非协调扩展逐层法(IXLWM)。通过大量的数值算例验证了本文建立的方法的正确性,并通过与原方法对比分析了本文方法的收敛性,同时根据Wilson非协调位移项的特点,研究了非协调位移项不同的引入策略(引入方向和引入范围)对收敛速度的影响,以及本文方法在不同弯曲变形程度下(含不同裂纹长度的矩形板,不同(边长/厚度)比值的方板和球壳)的收敛性能。研究结果表明:对于弯曲问题,采用适当的非协调位移项的添加策略,本文方法的收敛速度比原方法的收敛速度快。对于仅在局部发生弯曲变形的模型,局部添加的收敛效果比全局添加的收敛效果好。弯曲变形较大时,局部添加和全局添加的收敛速度相接近但是前者的效率更高。分析仅在局部发生小弯曲变形的模型时,在未发生弯曲变形区域添加的非协调自由度将导致计算结果偏大和振荡。所以对于本文建立的三种方法,非协调位移项的添加原则为:仅添加在发生弯曲变形区域和发生弯曲变形的方向。
[Abstract]:Composite laminated plate and shell are widely used in engineering, so there are a lot of theories about laminated plate and shell analysis and damage analysis. The extended layer-by-layer method combines the advantages of the layer-by-layer method and the extended finite element method, and provides an accurate analysis method for the damage study of composite laminated structures. However, in practical application, it is found that the convergence rate of extended layer-by-layer analysis of bending model is slow, especially in the analysis of large bending deformation, in order to achieve a certain accuracy, it is necessary to divide very fine grid. As a result, it will take a lot of computing time. In addition, for composite laminated plates, bending modes occur from time to time due to delamination and cracks. In this paper, the advantages of Wilson nonconforming technique in analyzing bending deformation are used to improve the convergence speed of extended layer-by-layer method. The Wilson nonconforming technique is introduced into the extended finite element method, layer by layer method and extended layer by layer method, respectively. the nonconforming extended finite element method (IXFEM), nonconforming layer by layer method (ILWM) and the nonconforming extended layer by layer method (IXLWM). Are established. The correctness of the proposed method is verified by a large number of numerical examples, and the convergence of the proposed method is compared with the original method. At the same time, according to the characteristics of Wilson nonconforming displacement term, The influence of different introduction strategies of nonconforming displacement terms (introduction direction and range) on the convergence rate is studied, and the rectangular plates with different crack lengths under different bending deformation degrees are studied. Convergence performance of square plate and spherical shell with different side length / thickness ratio. The results show that the convergence speed of the proposed method is faster than that of the original method by using the appropriate strategy of adding nonconforming displacement terms for bending problems. For the model with only local bending deformation, the convergence effect of local addition is better than that of global addition. When the bending deformation is large, the convergence rate of local addition is close to that of global addition, but the efficiency of the former is higher. When the model with small bending deformation occurs only locally, the nonconforming degrees of freedom added in the region without bending deformation will lead to the calculation results being too large and oscillatory. Therefore, for the three methods established in this paper, the addition principle of nonconforming displacement term is: only in the bending deformation region and in the direction of bending deformation.
【学位授予单位】：中国民航大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB33
本文编号：2481674
[Abstract]:Composite laminated plate and shell are widely used in engineering, so there are a lot of theories about laminated plate and shell analysis and damage analysis. The extended layer-by-layer method combines the advantages of the layer-by-layer method and the extended finite element method, and provides an accurate analysis method for the damage study of composite laminated structures. However, in practical application, it is found that the convergence rate of extended layer-by-layer analysis of bending model is slow, especially in the analysis of large bending deformation, in order to achieve a certain accuracy, it is necessary to divide very fine grid. As a result, it will take a lot of computing time. In addition, for composite laminated plates, bending modes occur from time to time due to delamination and cracks. In this paper, the advantages of Wilson nonconforming technique in analyzing bending deformation are used to improve the convergence speed of extended layer-by-layer method. The Wilson nonconforming technique is introduced into the extended finite element method, layer by layer method and extended layer by layer method, respectively. the nonconforming extended finite element method (IXFEM), nonconforming layer by layer method (ILWM) and the nonconforming extended layer by layer method (IXLWM). Are established. The correctness of the proposed method is verified by a large number of numerical examples, and the convergence of the proposed method is compared with the original method. At the same time, according to the characteristics of Wilson nonconforming displacement term, The influence of different introduction strategies of nonconforming displacement terms (introduction direction and range) on the convergence rate is studied, and the rectangular plates with different crack lengths under different bending deformation degrees are studied. Convergence performance of square plate and spherical shell with different side length / thickness ratio. The results show that the convergence speed of the proposed method is faster than that of the original method by using the appropriate strategy of adding nonconforming displacement terms for bending problems. For the model with only local bending deformation, the convergence effect of local addition is better than that of global addition. When the bending deformation is large, the convergence rate of local addition is close to that of global addition, but the efficiency of the former is higher. When the model with small bending deformation occurs only locally, the nonconforming degrees of freedom added in the region without bending deformation will lead to the calculation results being too large and oscillatory. Therefore, for the three methods established in this paper, the addition principle of nonconforming displacement term is: only in the bending deformation region and in the direction of bending deformation.
【学位授予单位】：中国民航大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB33
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