Structural Engineering and Mechanics

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A new semi-analytical approach for bending, buckling and free vibration analyses of power law functionally graded beams

  • Du, Mengjie (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology) ;
  • Liu, Jun (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology) ;
  • Ye, Wenbin (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology) ;
  • Yang, Fan (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology) ;
  • Lin, Gao (State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology)
  • Received : 2021.01.13
  • Accepted : 2021.10.22
  • Published : 2022.01.25
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Abstract

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

Keywords

Acknowledgement

This research was supported by Grant 51779033 from the National Natural Science Foundation of China for which the authors are grateful.

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