A novel laminated power-law model for bending analysis of functionally graded plates with arbitrary material...

A novel laminated model for analyzing the bending problem of functionally graded materials with arbitrary characteristic variations is developed. Based on the mathematical principle that an arbitrary curve can be approximated by a series of continuous, piecewise power-law curves, a functionally graded material with arbitrarily continuous material property is modeled as a multi-layer medium. In this model, the elastic modulus within each layer follows a general power-law distribution, ensuring continuity of stress and displacement at the interfaces between adjacent sub-layers. A theoretical method for analyzing the bending problem of a simply supported functionally graded rectangular plates under arbitrary loadings is established using this model. Taking a rectangular plate subjected to double trigonometric loadings as an example, all displacement and stress components are obtained. Parameterized analysis shows that the change in the number of layers has an impact on the convergence of the calculation results, revealing a quantitative relationship between the number of layers and computational accuracy; Under the same layering conditions, the approximation effects of different gradient distribution models on the exact solution are compared. This proposed laminated model has excellent convergence characteristics and computational efficiency, providing a new and effective approach for the mechanical analysis of functionally graded material plate structures, and has important application value in fields such as aerospace.