Accurate analysis of the stress, strain, and deformation fields in the square ended adhesive layer or square ended sandwich structure core requires a full elasticity solution. To this end a polynomial Airy stress function that satisfies all displacement boundary conditions, all stress free boundary conditions, and point equilibrium is proposed. The remaining requirement of a full elasticity solution, strain compatibility, is satisfied through a Galerkin approximation of the biharmonic equation on the Polynomial Airy stress function. To explore the utility of this Biharmonic Polynomial solution, the stress fields are explored for the case of idealized simple shear. The peel, shear, and longitudinal normal stress fields are found to be finite, differentiable, and convergent throughout the domain including the sharp corners of the elastic medium. The resulting stress components are compared to the Goland-Reissner Model, the Closed Form Higher Order (CFHO) model, and the Decoupled Biharmonic (DB) model. It is found that previous models significantly underestimate the peak peel stress, and with it the peak von Mises stress and the peak Principal stress values that drive the failure envelope for ductile and brittle materials, respectively.

准确分析方端粘合层或方端夹心结构芯中的应力，应变和变形场需要完整的弹性解。为此，提出了满足所有位移边界条件，所有无应力边界条件和点平衡的多项式艾里应力函数。通过多项式Airy应力函数上双调和方程的Galerkin近似，可以满足完整弹性解决方案的其余要求，即应变相容性。为了探索该双调和多项式解的实用性，在理想化简单剪力情况下探索了应力场。发现剥离，剪切和纵向法向应力场在整个区域（包括弹性介质的尖角）都是有限的，可微的并且会聚。将所得应力分量与Goland-Reissner模型，闭式高阶（CFHO）模型和解耦双谐波（DB）模型进行比较。发现以前的模型明显低估了峰值剥离应力，峰值von Mises应力和峰值主应力值分别驱动了韧性和脆性材料的破坏包络线。