This article presents a different polynomial interpolation function based dynamic finite element model to study and analyze the mechanical behavior of bidirectional functionally graded beams under moving load. To improve the mechanical behavior of the functionally graded beam, material properties are assumed to be symmetrically distributed throughout the axial and transverse directions. The first order shear deformation theory is employed to incorporate the transverse shear strain. To overcome the shear locking phenomena with satisfying all true kinematic constrains and no need to assume new strain field, five noded beam element with ten degrees of freedom and different polynomial interpolation functions is used. Cubic polynomial interpolation functions are assumed for the transverse deflection while quadratic polynomials are used for both axial and rotational displacements. Equations of motion are developed using the virtual displacement principle. Finite elements stiffness, mass matrices and force vector are derived in explicit forms. The unconditionally stable Newmark technique is employed for the transient time response. The developed procedure is checked and compared with the available results and an excellent agreement is observed. The applicability of the developed numerical procedure is demonstrated and discussed. Effects of the geometrical, material characteristics, and the moving load speed on the mechanical behavior are investigated and discussed. Obtained results are supportive for the design and manufacturing of bidirectional functionally graded beam structures.

本文提出了一种基于动态有限元模型的不同多项式插值函数，以研究和分析双向功能梯度梁在移动载荷下的力学行为。为了改善功能梯度梁的机械性能，假设材料特性在轴向和横向上对称分布。采用一阶剪切变形理论来合并横向剪切应变。为了在满足所有真实运动学约束且无需假设新应变场的情况下克服剪切锁定现象，使用具有十个自由度和不同多项式插值函数的五节点梁单元。三次多项式插值函数用于横向偏转，而二次多项式用于轴向和旋转位移。运动方程是使用虚拟位移原理开发的。有限元刚度、质量矩阵和力矢量以显式形式导出。瞬态时间响应采用无条件稳定的 Newmark 技术。对开发的程序进行检查并与可用结果进行比较，并观察到极好的一致性。证明和讨论了所开发的数值程序的适用性。研究和讨论了几何、材料特性和移动负载速度对机械性能的影响。