In this paper, a new semi-analytical approach based on the scaled boundary finite element method (SBFEM) is proposed to solve buckling problem of functionally gradient material (FGM) sandwich beams. Material properties of each individual layer are assumed to be continuously graded along the thickness according to a power law function with respect to the volume fractions. Based on the layer-wise theory, the two-dimensional constitutive model is directly performed in the proposed formulations without any kinematic assumptions of plate theory. The buckling governing equations of FGM sandwich beams based on the SBFEM are derived using the weighted residual method and solved by the means of the eigenvalue analysis. The advantage of the present approach is that only the longitudinal dimension of the beam structure needs to be discretized using one-dimensional higher-order spectral element so that it can be dealt with as a one-dimensional mechanical system while maintaining the analytical characteristics in the thickness direction, which possesses a key feature to make structure modelling more effective and accuracy. To evaluate the validity of proposed formulations, a series of numerical examples involving the element convergence and parametric analysis are carried out and the results are compared with existing solutions available in open literature. The numerical studies confirm the accuracy and adaptability of the presented method for the buckling analysis of FGM sandwich plates.

为了解决功能梯度材料（FGM）夹层梁的屈曲问题，提出了一种基于比例边界有限元法（SBFEM）的半解析方法。假定每个单个层的材料属性根据相对于体积分数的幂律函数沿厚度连续分级。基于分层理论，二维本构模型直接在提出的公式中执行，而没有板理论的任何运动学假设。利用加权残值法推导了基于SBFEM的FGM夹层梁屈曲控制方程，并通过特征值分析求解。本方法的优点在于，仅需使用一维高阶谱元素离散化梁结构的纵向尺寸，以便可以将其作为一维机械系统处理，同时保持其分析特性。厚度方向，具有使结构建模更加有效和准确的关键特征。为了评估所提出的配方的有效性，进行了一系列涉及元素收敛和参数分析的数值示例，并将结果与​​开放文献中的现有解决方案进行了比较。数值研究证实了该方法对FGM夹层板屈曲分析的准确性和适用性。