Two-dimensional Green’s function for an isotropic equal-thickness double-layer structure - Jie Tong; Juan Li; Jiang Su; Ying-jie Liu (AIP Advances)
According to Green’s function for a half-infinite plane subjected to a concentrated force, a two-dimensional Green’s function is derived for an isotropic double-layer structure of equal thickness under a concentrated force applied above the surface. This derivation was based on the mirroring image method and Dirichlet’s principle of singularity. Initially, the characteristics of the equal-thickness double-layer structure were examined, leading to the formulation of the upper and lower surface and interface conditions of the computational structure. Subsequently, four series of harmonic functions were generated from ten harmonic functions using the general solutions to two harmonic functions. By substituting these four series functions into a two-dimensional general solution, eight recursive equations were derived. The equations were expressed through eight harmonic functions, which could be solved using the upper and lower surface conditions and interface connection conditions. The harmonic function under any force can be determined through Green’s function for an isotropic half-infinite plane structure, allowing for the computation of the displacement and stress fields of the isotropic double-layer structure with equal thickness. Finally, numerical examples were used to compare the interface calculation results of this study with the finite element method numerical results, demonstrating the validity of the algorithm. This method is computationally simple and converges quickly. Utilizing the principle of superposition, the stress fields and displacements of an isotropic finite element method equal-thickness double-layer structure can be solved for any directional force acting on the surface, providing a robust foundation for the engineering design and analysis of such problems.