基于一种新修正偶应力理论建立了微尺度平面正交各向异性功能梯度梁模型。模型中包含两个材料尺度参数,因此能够分别描述在两个正交方向上由尺度效应带来的不同大小弯曲刚度增强。基于最小势能原理推导了平衡方程和边界条件,并以自由端受集中载荷作用的悬臂梁为例给出了弯曲问题的解析解。该梁模型的控制方程以及解的形式和经典梁模型是一致的,只是在刚度项中增加了一项和尺度效应有关的项。算例结果表明:采用本文模型所预测的梁挠度总是小于经典理论的结果,即捕捉到了尺度效应。尺度效应会随着梁几何尺寸的减小而增大,并在梁的几何尺寸远大于尺度参数时逐渐消失。 A microscale planar orthotropic functional gradient beam model was established based on a new theory of even-induced stress. Since the model contains two material-scale parameters, it is possible to describe the different-size bending stiffness enhancements caused by the scale effect in two orthogonal directions, respectively. The equilibrium equations and boundary conditions are deduced based on the principle of minimum potential energy. An analytical solution to the bending problem is given by taking the free-end cantilever beam subjected to concentrated load as an example. The governing equations and solutions of the beam model are consistent with the classical beam model, except that a term related to the scale effect has been added to the stiffness term. The results show that the beam deflection predicted by this model is always smaller than that of the classical theory, that is, the scale effect is captured. The scale effect increases as the beam geometry decreases and disappears when the beam geometry is much larger than the scale parameter.