Linear bending of functionally graded beams by differential quadrature method

2nd International Symposium on Resource Exploration and Environmental Science

生态环境科学

Jiao, Pengfei^1,2 ; Wang, Youzhi^1 ; Xu, Gangnian^1 ; Zhang, Fengping^1 ; Yuan, Quan^1 ; You, Weijie^1

School of Civil Engineering, Shandong University, Ji'nan

250061, China^1

Highway Bureau, Shandong Provincial Department of Transportation, Ji'nan

250002, China^2

关键词: Classical beam theory;    Differential quadrature methods;    Functionally graded;    Functionally graded beams;    Governing equations;    Numerical solution;    Total potential energy;    Transverse shear deformation;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/170/2/022160/pdf
DOI  :  10.1088/1755-1315/170/2/022160

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Based on the first-order shear deflection and classical beam theory, the linear bending of functionally graded (FG) beams is analyzed by applying the differential quadrature method (DQM). First, using the principle of total potential energy, the governing equations of the FG beams subjected to a distributed lateral force are derived according to two different beam theories. To calculate the numerical solutions of static linear bending problem, the dimensionless boundary conditions and differential equation which are used to discretize by DQ method. Static deflection curves and load-central deflection curves is generated considering two different beam theories. The influences of the power law index, transverse shear deformation and the distributed lateral force on the linear bending of the FG beams under cinditions of the simply supported and the clamped-clamped boundaries are analytically investigated in detail.