A Finite Element Formulation for Analyzing the Nonlinear Static Response of Bi-functionally Graded Microbeam Resting on Elastic Foundation Under Various Loads

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 2DFG-McrB resting on EF under four different loads. The governing equations are established using the principle of minimum potential energy, incorporating the RBT and geometric nonlinearity based on the von Kármán assumptions. A weak-form finite element method is developed and solved iteratively through the Newton-Raphson method. The proposed formulation is validated against benchmark results from the literature, demonstrating its accuracy and computational efficiency. Furthermore, a comprehensive parametric study is conducted to evaluate the effects of geometrical dimensions, material properties, foundation stiffness, length-scale parameters, and BCs on the nonlinear response of 2DFG-McrBs. The findings provide valuable insights for the design and analysis of McrBs in engineering applications and serve as a basis for future studies on advanced microstructures.

Keywords

Main Subjects

References

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Mechanics of Advanced Composite Structures
Volume 13, Issue 1 - Serial Number 27
In Progress
April 2026
Pages 227-243

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