Large displacement behaviour of tapered cantilever Euler–Bernoulli beams made of functionally graded material

• Published in: Applied mathematics and computation 2014-06, Vol.237, p.340-355
• Main Author: Nguyen, Dinh Kien
• Format: Article
• Language: English
• Subjects: Cantilever beams; Computation; Displacement; Euler-Bernoulli beams; Finite element method; Functionally graded material; Functionally gradient materials; Large displacement; Mathematical analysis; Mathematical models; Power-law distribution; Tapered beam
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.03.104

•Derived a nonlinear beam element for large displacement analysis.•Tapered Euler–Bernoulli beams made of functionally graded material can be analysed.•Material property varies in the thickness direction according to a power-law distribution.•Numerical examples show fast convergence and accurate results with a few elements.•Influence of material inhomogeneity, taper ratio and taper type is numerically studied and highlighted. The large displacement behaviour of tapered cantilever Euler–Bernoulli beams made of functionally graded material subjected to end forces is studied by the finite element method. The effective Young’s modulus of the beams is assumed to be graded in the thickness direction by a power-law distribution. Based on the co-rotational approach, a finite element formulation is derived and employed in the study. An incremental/iterative procedure in combination with the arc-length control method is used in computing the large displacement response of the beams. The numerical results show that the derived formulation is capable to give accurate results by using just several elements. A parametric study is given to highlight the influence of the material inhomogeneity, taper ratio and taper type on the large displacement behaviour of the beams. The large displacement behaviour of beams composed of different constituent materials is also investigated and highlighted.