Coupled systems mechanics

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Application of a new improved Airy polynomial function for FGM cantilever beams under concentrated load

  • Received : 2024.12.27
  • Accepted : 2025.05.21
  • Published : 2025.04.25
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Abstract

This paper addresses the plane stress problem of a cantilever functionally graded beam subjected to concentrated load. The material properties of the beam vary continuously through thickness, according to a power-law distribution of volume fraction. The existing solution focuses on resolving differential equations, but a new Airy function proposal is proposed. The paper examines the effect of material graduation on the degree of polynomial degree. A simple formulation developed to predict stress and displacement distributions relative to structural problems. The proposed model validated by comparison with existing literature, ensuring stability and resistance of the materials. A numerical example presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.

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References

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