高性能边界元方法及其在航天器结构分析中的应用

As a result of high strength and good anti fatigue performance, the stiffened plate and shell structure has been widely applied in all kinds of spacecraft. So far in the design and analysis of stiffened plate and shell structures, the finite element method (FEM) are usually used, which are based on the theory of plates and shells. The plates and shells are divided into various plate elements and shell elements, and the stiffened ribs are divided into a variety of beam elements. However, since this analysis method cannot accurately calculate the local stress at the connecting between the ribs and shells, it will reduce the effectiveness of strength analysis. The project will establish a high performance boundary element method, which can effectively calculate the true local stress at the junction of the ribs and plates/shells..The concrete research contents include the followings..(1) To develop a high accuracy boundary element method (HCBEM), the various types of compatibility elements are used to keep the real geometry of structure boundary, and some special techniques are adopted to ensure the integration accuracy of the product of fundamental solution and interpolation function over the boundary elements..(2) Combining the ACA or fast multipole algorithm and the HCBEM, a high performance boundary element method (HPBEM) will be developed, which not only greatly increase the calculation speed, but also keep calculation precision of fast algorithms. .(3) Based on the previous work, the presented HPBEM will be used to fulfill the analysis of the true local stress at the junction of the ribs and plates/shells. A HPBEM analysis software with proprietary intellectual property rights will be also developed, and it will become the necessary complement to FEM software in spacecraft structure analysis.

由于加筋板壳结构具有强度高、抗疲劳性能好等优点，在各种航天器结构中得到了广泛应用。目前在加筋板壳结构的设计分析中通常采用有限元法，即板壳部分基于板壳理论划分为各种板壳单元，加强筋则基于梁理论划分为各种梁单元。但是这种分析方法无法准确计算加强筋与板壳连接处的局部应力变化，从而降低了强度分析的有效性。本项目将建立一种高性能边界元法，它能有效地处理加强筋与板壳连接处的真实局部应力分布。具体研究内容包括：（1）发展高精度边界元计算方法，其中包括为模拟边界实际形状所建立的各种类型的变形协调单元，并且能够充分保证单元上核函数与形函数乘积积分的精度；（2）将ACA和快速多极算法与高精度边界元法相结合，建立一种能同时保证计算精度和计算速度的高性能边界元法；（3）用高性能边界元法实现真实加筋板壳结构的局部应力分析。在此基础上进一步研发具有自主知识产权的高性能边界元分析软件，为航天结构分析与设计提供有效手段。

本项目旨在建立一种新的高性能边界元法，使其能有效地计算梁板壳结构的局部真实应力。具体研究成果主要包括：（1）发展了高精度边界元计算方法，其中包括为模拟边界实际形状所建立的各种类型的变形协调单元，为保证单元上核函数与形函数乘积积分精度的各种积分计算方案；（2）将GMRE快速迭代求解技术与高精度边界元法相结合，建立了一种能同时保证计算精度和计算速度的高性能边界元法；（3）针对细长梁结构GMRES求解方法收敛性明显下降的问题，我们提出了一种近奇异积分的对偶合并预处理方法，该方法在收敛性方面明显优于传统的稀疏矩阵近似逆预处理技术；（4）用高性能边界元法实现了真实加筋板壳结构的局部应力分析。在此基础上进一步研发了具有自主知识产权的高性能边界元分析软件，为航天结构的分析与设计提供了有效手段。