This article presents an effective computational approach that incorporates a quasi-brittle damage model into the isogeometric analysis of plates made of functionally graded materials. The plate kinematics is represented by a third-order shear deformation theory for higher accuracy. A coupling nonlocal equivalent strain field is introduced on the plate neutral surface to control the softening behavior. The utilization of the neutral surface in functionally graded plates enables the use of a single damage parameter over each plate cross-section. As a consequence, plate stiffness matrices can be calculated analytically, which simplifies the proposed damage model and its computer implementation. The discretization of the problem domain is based on basis functions generated from the non-uniform rational B-splines (NURBS) which are used for both geometric representation and field variable approximations, i.e., displacement and nonlocal equivalent strain. Owing to the high-order continuity of the NURBS basis functions, local features such as fracture damage zones can be resolved accurately. The performance of the proposed approach is demonstrated through several numerical examples under different loading configurations and compared with results from other approaches.

本文提出了一种有效的计算方法，该方法将准脆性损伤模型纳入功能梯度材料制成的板的等几何分析中。板运动学由三阶剪切变形理论表示，以实现更高的精度。在板中性表面上引入耦合非局部等效应变场，以控制软化行为。通过在功能梯度板中使用中性表面，可以在每个板横截面上使用单个损伤参数。因此，可以分析计算板刚度矩阵，从而简化了提出的损伤模型及其计算机实现。即，位移和非局部等效应变。由于NURBS基函数的高阶连续性，因此可以精确地解决局部特征，例如断裂损坏区域。通过在不同载荷配置下的几个数值示例证明了该方法的性能，并与其他方法的结果进行了比较。