R-function method and variational method for the bending problem of functionally graded plates with fixed supports...

Area of Science:

• * Mechanical Engineering
• * Materials Science
• * Computational Mechanics

Background:

• * Analytical solutions for functionally graded plate bending are limited to simple boundary conditions.
• * Traditional numerical methods struggle with complex geometries.
• * The R-function method offers a way to handle intricate boundary shapes.

Purpose of the Study:

• * To integrate R-function theory with the variational method for analyzing functionally graded plates.
• * To develop a method capable of addressing complex boundary conditions in plate bending problems.
• * To provide a robust numerical tool for functionally graded plate analysis.

Main Methods:

• * Integration of R-function theory for implicit region representation.
• * Application of the variational method for deriving governing equations.
• * Construction of trial functions suitable for complex boundary conditions.

Main Results:

• * Successful application to rectangular, U-shaped, and L-shaped functionally graded plates.
• * Validation of the method's accuracy and feasibility through numerical examples.
• * Good agreement with existing literature and finite element method (FEM) results.

Conclusions:

• * The combined R-function and variational method is effective for functionally graded plate bending with complex boundaries.
• * This approach enhances the capability of numerical methods for intricate engineering problems.
• * The study provides a validated and accurate method for analyzing complex plate structures.