Bending Analysis of Functionally Graded Thick Plates on Elastic Foundations by Boundary Element Method

Background and Objectives: Currently, Functionally Graded Materials (FGMs) are garnering significant attention in engineering due to their versatile applications in structural components, especially in plate structures. Their properties, which vary continuously with thickness, enable the tailoring of mechanical properties and resistance to meet specific operational needs. Analyzing the bending behavior of thick FGM plates on elastic foundations is complex. It requires consideration of the interactions between the plate and the foundation, as well as the implications of variations in material properties with thickness. Therefore, this topic constitutes a crucial area of study in this research. Although the Finite Element Method (FEM) and other analytical approaches have been extensively developed to analyze the bending of thick FGM plates on elastic foundations, they continue to encounter limitations in managing complex boundary conditions and structural shapes. Consequently, in this research, the Boundary Element Method (BEM) has been developed as an alternative for analyzing thick FGM plates on elastic foundations. This method efficiently reduces the number of variables required for calculations and can effectively handle diverse boundary conditions and shapes. This advancement significantly enhances the potential of the Boundary Element Method to deliver accurate and reliable results in the analysis of complex structures.

Methodology: The governing equations and boundary conditions for this study are derived using the principle of virtual work, based on the first-order shear deformation plate theory. The properties of Functionally Graded Materials (FGMs) are modeled using a Power Law distribution. The method presented has been developed using the concept of the Analog Equation Method, where the differential equations of the original problem are substituted with three Poisson’s equations under fictitious forces, maintaining the original boundary conditions. These fictitious forces are generated using techniques based on the Boundary Element Method and approximated using radial basis functions. The reliability of the proposed method has been assessed by comparing the results of this research with outcomes from other established approaches.

Main Results: The numerical results obtained from the method presented here are highly accurate and precise when compared to other related research, demonstrating convergence of the solution as the number of boundary elements and internal nodes increases. Furthermore, it effectively analyzes thick FGMs plates on elastic foundations under complex conditions, such as an elastic support and elastic restraint, or plates with various shapes. Such complex problem analysis has not been found in previous research studies.

Conclusions: This research developed the Boundary Element Method (BEM) in conjunction with the Principle of Analog Equation to analyze the bending of complex thick plates made from Functionally Graded Materials (FGMs) resting on elastic foundations, considering both the boundary conditions and the plate shapes. The results demonstrate the accuracy and efficiency of the proposed methods, capable of accurately simulating the interactions and effects of material properties and various parameters on the bending response of the plates.

Practical Application: This study proposes an effective method for analyzing the bending of thick plates made from Functionally Graded Materials (FGMs) on elastic foundations, capable of analyzing plates with complex shapes and boundary conditions that are common in real-world applications. This allows for the safe and efficient design of such structures.