Semi-analytical simulation method for bi-directional FGM cantilever beam under stochastically distributed load

doi:10.19936/j.cnki.2096-8000.20250928.003

Abstract

Abstract: In order to study the mechanical behavior of bi-directional functionally graded material (FGM) cantilever beam under stochastically distributed load, a semi-analytical method of high precision and efficiency is developed in this paper. Firstly, the physical model of the bi-directional FGM cantilever beam is introduced, and then the basic control equations of the cantilever beam subjected to stochastically distributed load are derived. Then, iterative solution of the equations is complemented through MATLAB programming. Based on this, a case study of unidirectional/bi-directional FGM cantilever beams subjected to pure bending load or uniformly distributed load is carried out, where the results are compared with the exact solution, Timoshenko beam theory results and graded finite element method results, indicating that the proposed method has good convergence and high accuracy. Finally, the proposed method is used to simulate and analyze the mechanical behavior of bi-directional FGM cantilever beams under linearly distributed load, sinusoidally distributed load or stochastically distributed load. The results obtained are in good agreement with the simulation results of the gradient finite element method, where the maximum relative errors for deflection and stress are within 2.11% and 3.39%, respectively.

Key words: bi-directional FGM, cantilever beam, stochastically distributed loads, semi-analytical method, finite element method, composites

CLC Number:

TB332

ZHANG Long, ZHANG Wei, FAN Juntao, LIAO Wenlin. Semi-analytical simulation method for bi-directional FGM cantilever beam under stochastically distributed load[J]. COMPOSITES SCIENCE AND ENGINEERING, 2025, 0(9): 16-26.

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