Differential quadrature method of nonlinear bending of functionally graded beam

International Conference on Mechanical Engineering and Applied Composite Materials

机械制造;材料科学

Gangnian, Xu^1 ; Liansheng, Ma^2 ; Wang, Youzhi^1 ; Quan, Yuan^1 ; Weijie, You^1

School of Civil Engineering, Shandong University, Ji'nan

250061, China^1

School of Science, Lanzhou University of Technology, Lanzhou

730050, China^2

关键词: Differential quadrature methods;    Functionally graded;    Functionally graded beams;    Non-linear bending;    Numerical results;    Partial differential;    Stationary potentials;    Transverse shear deformation;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/307/1/012058/pdf
DOI  :  10.1088/1757-899X/307/1/012058

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.