Numerical Solution of Bending Problem of a FGM Cantilever Beam with Large Deformation
Nonlinear bending problem of FGM cantilever beam under distributed load are discussed in this paper. Based on the large deformation theory and considering the axial extension of the beam, the equilibrium equations with geometric nonlinearity of a FGM beam subjected to distributed load are established. They consist of a boundary value problem of ordinary differential equations with strong non-linearity, in which seven unknown functions are included and the arc length of the deformed axis is considered as one of the basic unknown functions. By using shooting method and analytical continuation, the nonlinear boundary-value problem is numerically solved as well as the non-linear bending characteristic curves of the deformed beam versus the load are presented.
Guojun Zhang and Jessica Xu
Q. L. Li and S. R. Li, "Numerical Solution of Bending Problem of a FGM Cantilever Beam with Large Deformation", Advanced Materials Research, Vols. 160-162, pp. 503-506, 2011