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SummaryElement differential method (EDM), as a newly proposed numerical method, has been applied to solve many engineering problems because it has higher computational efficiency and it is more stable than other strong‐form methods. However, due to the utilization of strong‐form equations for all nodes, EDM become not so accurate when solving problems with abruptly changed boundary conditions. To overcome this weakness, in this article, the weak‐form formulations are introduced to replace the original formulations of element internal nodes in EDM, which produce a new strong‐weak‐form method, named as weak‐form element differential method (WEDM). WEDM has advantages in both the computational accuracy and the numerical stability when dealing with the abruptly changed boundary conditions. Moreover, it can even achieve higher accuracy than finite element method (FEM) in some cases. In this article, the computational accuracy of EDM, FEM, and WEDM are compared and analyzed. Meanwhile, several examples are performed to verify the robustness and efficiency of the proposed WEDM.

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With the rapid development of hypersonic vehicles in recent years, high-temperature seal technology has become more and more essential. Recently, a rope-sealed structure with braided ceramic fibres has been designed for hypersonic vehicles. The ceramic fibres in the structure have the characteristics of high temperature strength, so that they make the sealed structure suitable for working under a high temperature. Meanwhile, when subjected to an external force, braided fibres can produce a buffer force at the ceramic interface, so that it can maintain the good performance of the whole sealed structure. But up to now, only a few researches have been conducted on this kind of structures. In this paper, a simplified thermal-mechanical seepage coupling model is proposed to simulate the complicated physical process for this kind of structures. Meanwhile, a new numerical method called element differential method (EDM) is used to calculate the coupling problem because it has great advantages in solving multiphysics coupling problems. What is more, some experiments are used to obtain the leakages when the sealed structure is under service. And finally, by referring the experimental results, the authors establish a series of material parameter relationships for the sealed structure and also verify the reasonability of the proposed multi-physics coupling model.