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

Abstract

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.

Geometrically nonlinear analysis of sandwich composite beams reinforced by agglomeration carbon nanotubes

“…The beam element based on the above linear interpolation functions, however encounters the shear locking problem [4]. In order to overcome this problem, the reduced integration technique, namely one-point Gauss quadrature, is employed herewith to evaluate the strain energy of the element.…”

“…For nonlinear analysis of sandwich beams, Nguyen and Tran [3] performed a large displacement analysis of functionally graded (FG) sandwich beams and frames using a co-rotational Euler-Bernoulli beam element. Hoai et al [4] derived a nonlinear finite beam element for studying the large displacements of FG sandwich beams, considering the effect of environment temperature rise. The influence of various homogenization schemes on large deflections of dual-phase FG sandwich beams is investigated by Nguyen et al [5] using a nonlinear finite element procedure.…”