Abstract This paper is focused on the application of a novel reproducing kernel particle finite strip method (RKP-FSM) for the static, mechanical and thermal buckling, and free vibration analyses of rectangular functionally graded (FG) plates with different boundary conditions and internal supports. Conventional reproducing kernel particle method (RKPM) is incorporated into the finite strip method (FSM), and the governing equations are derived based on the first-order shear deformation theory (FSDT). As a convenient approach, boundary conditions are imposed using a simple method based on the RKPM correction function and the essence of the FSDT displacement field. Several examples are studied using this method, and the results are compared to those obtained from other numerical methods. The proposed method is also extended to consider different support geometries and complex inner conditions, and the results are validated using COMSOL finite element software. The shear-locking error, which occurs when considering C0 plate theories, is noticeably reduced by considering the RKPM parameters in the finite strip formulation.

中文翻译：

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再生核粒子有限条法在不同边界条件和不同内支撑的FG板静力、稳定性和自由振动分析中的应用

摘要 本文重点介绍了一种新的再生核粒子有限条法 (RKP-FSM) 在具有不同边界条件和内部支撑的矩形功能梯度 (FG) 板的静态、机械和热屈曲以及自由振动分析中的应用。 . 将传统的再生核粒子法（RKPM）纳入有限条带法（FSM），根据一阶剪切变形理论（FSDT）推导出控制方程。作为一种方便的方法，使用基于 RKPM 校正函数和 FSDT 位移场本质的简单方法施加边界条件。使用这种方法研究了几个例子，并将结果与​​其他数值方法获得的结果进行了比较。所提出的方法还扩展到考虑不同的支撑几何形状和复杂的内部条件，并使用 COMSOL 有限元软件验证结果。考虑 C0 板理论时出现的剪切锁定误差通过考虑有限条带公式中的 RKPM 参数显着降低。