A finite element formulation for analyzing the nonlinear static response of bi-functionally graded microbeam resting on elastic foundation under various loads

Articles in Press

Document Type : Research Article

Authors

Faculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi, Vietnam,

Abstract

The main goal of this paper is to introduce a finite element formulation to investigate the nonlinear static response of the bi-functionally graded microbeam (2DFG-McrB) resting on an elastic foundation (EF). The analysis employs a weak-form finite element formulation based on RBT and the Kármán assumption. The equations of motion are derived using Hamilton’s principle and solved using the Newton-Raphson iteration method. The effectiveness and accuracy of the proposed method are validated by comparison with existing results in the literature. In addition, parametric studies are conducted to examine the influence of geometrical parameters, material properties, foundation stiffness, length-scale parameters, and boundary conditions (BCs) on the nonlinear static response of 2DFG-McrB resting on an EF. The numerical and graphical results in this study are expected to be useful for the calculation and design of microbeams resting on EF under various loads in engineering practice as well as providing initial results for further studies.

Keywords

Main Subjects

Mechanics of Advanced Composite Structures

Articles in Press, Accepted Manuscript
Available Online from 17 July 2025

Files

Share

How to cite

Statistics