New Shape Function for the Bending Analysis of Functionally Graded Plate

Area of Science:

• Mechanical Engineering
• Materials Science
• Structural Analysis

Background:

• Functionally graded materials (FGMs) offer tailored material properties through thickness.
• Analyzing thick and moderately thick plates requires advanced shear deformation theories.
• Elastic foundations significantly influence plate behavior under transverse loads.

Purpose of the Study:

• To present a high-order shear deformation theory for bending analysis of functionally graded plates.
• To develop and validate a new shape function for improved accuracy.
• To create a MATLAB program for predicting FGM plate behavior.

Main Methods:

• Application of a novel high-order shear deformation theory.
• Development of a new shape function and comparison with 13 existing functions.
• Validation against third-order shear deformation theory and 3D elasticity theories.
• Implementation in MATLAB for analysis and prediction.

Main Results:

• The developed high-order shear deformation theory provides accurate bending analysis for FGM plates.
• The new shape function demonstrates superior performance compared to existing ones.
• The MATLAB code effectively predicts FGM plate behavior under various conditions.

Conclusions:

• The high-order shear deformation theory is effective for analyzing FGM plates.
• Transversal shear deformation, aspect ratio, and material distribution significantly impact plate behavior.
• The developed methodology and code offer a reliable tool for FGM plate analysis.