Large displacements of FGSW beams in thermal environment using a finite element formulation

Bui Thi Thu Hoai, Nguyen Dinh Kien, Tran Thi Thu Huong, Le Thi Ngoc Anh
Author affiliations


  • Bui Thi Thu Hoai Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • Nguyen Dinh Kien Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
  • Tran Thi Thu Huong Phenikaa University, Hanoi, Vietnam
  • Le Thi Ngoc Anh Institute of Applied Information and Mechanics, Ho Chi Minh city, Vietnam



FGSW beam, total Lagrange formulation, reduced integration, thermal environment, large deflection analysis


The large displacements of functionally graded sandwich (FGSW) beams in thermal environment  are studied using a finite element formulation. The beams are composed of three layers, a homogeneous core and two functionally graded face sheets with volume fraction of constituents following a power gradation law. The material properties of the beams are considered to be temperature-dependent.  Based on Antman beam model and the total Lagrange formulation, a two-node nonlinear beam element taking the effect of temperature rise into account  is formulated and employed in the study. The element with explicit expressions for the internal force vector and tangent stiffness matrix is derived using linear interpolations and reduced integration technique to avoid the shear locking. Newton-Raphson based iterative algorithm is employed in combination with the arc-length control method to compute the large displacement response of a cantilever FGSW beam subjected to end forces. The accuracy of the formulated element is confirmed through a comparison study. The effects of the material inhomogeneity, temperature rise and layer thickness ratio on the large deflection response of the beam are examined and highlighted.


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How to Cite

B. T. T. Hoai, N. D. Kien, T. T. T. Huong and L. T. N. Anh, Large displacements of FGSW beams in thermal environment using a finite element formulation, Vietnam J. Mech. 42 (2020) 43–61. DOI:



Research Article

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