This paper is devoted to numerical investigations on mechanical behavior of cracked composite functionally graded (FG) plates. We thus develop an efficient adaptive approach in terms of the extended isogeometric analysis (XIGA) enhanced by locally refined non-uniform rational B-spline (LR NURBS) for natural frequency and buckling analysis of cracked FG Mindlin–Reissner plates. In this setting, the crack geometries, which are described by the level sets, are independent of the computational mesh; and the LR NURBS basis functions, which have the abilities of local refinement and modeling the complex shape, are used as the shape functions of XIGA. According to the recovered stresses of the first buckling or free vibration mode, a posteriori error estimator for driving the adaptive process is defined. The accuracy can be effectively improved through adaptive local refinements, demonstrated through numerical experiments with complex geometries. Compared with uniform global refinement, XIGA based on adaptive local refinement has the characteristics of high precision at low cost and fast convergence rate. The effects of some factors such as crack length and location, plate thickness, gradient index, boundary condition, loading type, etc. on critical buckling loads and natural frequencies are investigated.

本文致力于裂纹复合功能梯度板的力学行为的数值研究。因此，根据扩展的等几何分析（XIGA），我们开发了一种有效的自适应方法，该方法通过对局部FG Mindlin-Reissner板的固有频率和屈曲分析进行局部细化的非均匀有理B样条（LR NURBS）进行了增强。在这种设置下，由级别集描述的裂缝几何形状与计算网格无关；它与计算网格无关。具有局部细化和建模复杂形状能力的LR NURBS基函数被用作XIGA的形状函数。根据第一屈曲或自由振动模式的恢复应力，定义了用于驱动自适应过程的后验误差估计器。通过对复杂几何形状进行数值实验可以证明，通过自适应局部改进可以有效地提高精度。与统一的全局细化相比，基于自适应局部细化的XIGA具有精度高，成本低，收敛速度快的特点。研究了裂纹长度和位置，板厚，梯度指数，边界条件，载荷类型等因素对临界屈曲载荷和固有频率的影响。