Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method

• Published in: Applied mathematics and mechanics Vol. 40; no. 10; pp. 1375 - 1386
• Main Authors: Lin, Xin, Huang, Yixin, Zhao, Yang, Wang, Tianshu
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.10.2019; Springer Nature B.V; School of Astronautics, Harbin Institute of Technology, Harbin 150001, China%School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Cantilever beams; Classical Mechanics; Configurations; Deformation analysis; Exact solutions; Finite element method; Fluid- and Aerodynamics; Functionally gradient materials; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Modulus of elasticity; Partial Differential Equations; 74K10; O343; TB121; large deformation beam; homotopy analysis method (HAM); axially functionally graded (AFG) material; Euler-Bernoulli beam
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-019-2515-9

Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.