Thermal analysis for plate structures using a transformation BEM based on complex poles - Zhong, Yudong; Xie, Guizhong; Geng, Hongrui; Hou, Junjian; Zhao, Dengfeng; He, Wenbin (Computers & mathematics with applications (1987), 2024)
In this paper, according to the element discretization characteristic of the geometric model, a complex function theory based transformation boundary element method is proposed to perform the steady-state thermal analysis of plate structures. The numerical implementation of the proposed method can be attributed to a numerical integration problem in element analysis, which is mainly divided into the following two steps: firstly, a bidirectional transformation method based on distance function and complex function is proposed to remove the weak singularities of the fundamental solution in integral equation, which is suitable for the weakly singular integrals of narrow strip discrete elements; secondly, a dual sinh method based on complex poles is developed to remove the influence of the nearly singular integrals in the analysis of the plate structures. With this method, the numerical integration in the integral equation can be accurately evaluated, which ensures the accurate calculation of the thermal physical variables of the plate structures. Several numerical examples are presented and discussed to prove the accuracy and versatility of the presented method. The results show that the presented method has the superiority of dealing with plate structure problems.