Thermal analysis of a perforated laminated plate with multiple random elliptical holes by specially formulated finite elements

• Published in: Applied mathematical modelling 2024-06, Vol.130, p.401-418
• Main Authors: Lin, Wan-Qing, Chen, Junqi, Lei, Yongpeng, Wang, Hui, Dong, Qinxi
• Format: Article
• Language: English
• Subjects: Elliptical hole; Hybrid variational functional; Perforated laminated plate; Special element; Special fundamental solutions
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2024.03.014

•Heat conduction in perforated laminated plate by elliptical holes is solved using formulated special elements.•Special fundamental solutions are derived using Stroh formula and conformal mapping.•Special element containing a rotated elliptical hole is formulated in the concept of hybrid finite element.•Meshing effort around hole region is greatly alleviated and element boundary integration is featured.•The accuracy, efficiency and flexibility of the present special element are demonstrated. The high-efficient and accurate analysis of anisotropic composite media weakened by a large amount of holes or cuts is still a great challenge in practical composite engineering. In this work, specially-proposed polygonal finite element enclosing an arbitrarily oriented elliptical hole in general anisotropic composite media is formulated for thermal analysis in the framework of hybrid finite element theory. Two independent temperature field approximations are defined for the present special element: Intra-element temperature field and element frame temperature field. The former defined inside the element is written in the form of truncated summation of the weighted special fundamental solutions, which are derived using the Stroh complex theory and conformal mapping whilst the latter is implemented by the conventional shape function interpolation. Then the hybrid variational functional is employed to combine them together to generate an element stiffness equation with respect to nodal temperature and an optional relationship between the interpolation coefficients. The element stiffness matrix is symmetric and involves element boundary integrals only. Compared to the traditional finite element, the distinctive element-boundary-integral and enclosed-elliptical-hole features make the present element significantly improve the meshing effort around an elliptical hole by reducing the number of elements and decreasing the meshing difficulty, and more importantly, effectively capture the critical variation of physical fields around the elliptical hole without locally-refined meshes. Moreover, the present special element can be incorporated directly into the conventional finite element system without any difficulty for extensive analysis. Finally, several typical examples are simulated by the present special elements to demonstrate their effectiveness.