A finite difference formulation is developed for the stress analyses in orthotropic three-layer composite beams with mono-symmetrical cross-sections under various force boundary and loading conditions. Four interfacial shear and peeling stress fields at material interfaces are assumed as unknown functions. Based on shear stress flow equilibrium conditions, three groups of stress fields including transverse shear, transverse normal and longitudinal normal stresses in the beam, the plate and the adhesive layer are expressed in terms of the unknown functions. A set of compatibility equations and corresponding boundary conditions are then derived from a variational principle of complementary strain energy and solved by a finite difference technique. The present theory eliminates kinematic assumptions of equal curvatures for the beam and the plate, it satisfies the infinitesimal stress equilibrium conditions of the interfacial shear and peeling stresses at material interfaces, and it captures the longitudinal normal stresses in the adhesive. By comparing to numerical and analytical solutions, the present theory is a solution for the prediction of concentrated transverse shear and transverse normal (peeling) in the adhesive occurring near the plate ends. Based on the present theory, a parametric study is conducted to quantify the effects of the strengthening length, thickness, and elasticity moduli of the FRP plate and adhesive layer on the peak values of the interfacial shear and peeling stresses.

为在各种力边界和载荷条件下具有单对称横截面的正交异性三层复合梁的应力分析开发了有限差分公式。材料界面处的四个界面剪切和剥离应力场被假定为未知函数。基于剪应力流平衡条件，用未知函数表示梁、板和胶层中的横向剪应力、横向法向应力和纵向法向应力三组应力场。然后从互补应变能的变分原理导出一组兼容性方程和相应的边界条件，并通过有限差分技术求解。本理论消除了梁和板曲率相等的运动学假设，它满足材料界面处界面剪切应力和剥离应力的无穷小应力平衡条件，并捕获粘合剂中的纵向法向应力。通过与数值解和解析解的比较，本理论是预测在板端附近发生的粘合剂中集中横向剪切和横向法线（剥离）的解。基于现有理论，进行了参数研究，以量化 FRP 板和胶粘剂层的加强长度、厚度和弹性模量对界面剪切和剥离应力峰值的影响。通过与数值解和解析解的比较，本理论是预测在板端附近发生的粘合剂中集中横向剪切和横向法线（剥离）的解。基于现有理论，进行了参数研究，以量化 FRP 板和胶粘剂层的加强长度、厚度和弹性模量对界面剪切和剥离应力峰值的影响。通过与数值解和解析解的比较，本理论是预测在板端附近发生的粘合剂中集中横向剪切和横向法线（剥离）的解。基于现有理论，进行了参数研究，以量化 FRP 板和胶粘剂层的加强长度、厚度和弹性模量对界面剪切和剥离应力峰值的影响。