Abstract A material-based higher-order shear beam model is proposed for accurate analyses of functionally graded (FG) beams with arbitrary material distribution through thickness. Distinct from the existing higher-order shear beam models, the shear function of the present model is dependent on the material distribution. The specific form of this material-based shear function is described by a piecewise linear interpolation field and determined by ensuring the consistency of transverse shear stress distributions between Euler-Bernoulli beam theory and the higher-order shear beam theory. Based on the proposed beam model, a 3-node beam finite element is developed for static and buckling analyses. Numerical examples are studied to visualize the accuracy and effectiveness of the proposed model and finite element. Solutions of static displacements and critical loads obtained by various beam elements including the proposed element, the existing displacement-based beam elements and the mixed higher-order shear beam element are compared. The accuracy loss of the existing higher-order shear beam models is discussed. As demonstrated by the results, the proposed beam model and finite element have excellent solution accuracy and desirable applicability.

中文翻译：

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一种基于材料的高阶剪切梁模型，用于精确分析具有任意材料分布的 FG 梁

摘要 提出了一种基于材料的高阶剪切梁模型，用于准确分析具有任意材料厚度分布的功能梯度 (FG) 梁。与现有的高阶剪切梁模型不同，本模型的剪切函数取决于材料分布。这种基于材料的剪切函数的具体形式由分段线性插值场描述，并通过确保欧拉-伯努利梁理论和高阶剪切梁理论之间横向剪应力分布的一致性来确定。基于所提出的梁模型，开发了用于静态和屈曲分析的 3 节点梁有限元。数值例子被研究以可视化所提出的模型和有限元的准确性和有效性。比较了各种梁单元（包括所提出的单元、现有的基于位移的梁单元和混合高阶剪切梁单元）获得的静态位移和临界载荷的解。讨论了现有高阶剪切梁模型的精度损失。结果表明，所提出的梁模型和有限元具有出色的求解精度和理想的适用性。