Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator

Abstract

A non-local numerical model for large deformation analysis of functionally graded beam (FGB) with variable cross-section is presented by using peridynamic differential operator (PDDO) in this paper. The nonlinear equilibrium equation and boundary condition of FGB with variable cross-section are reformulated from the local differential form into the non-local integral form based on PDDO. By employing variational analysis, Lagrange multiplier method, and Newton-Raphson method, the non-local governing equations can be solved with iterations. The proposed method is applied to the large deformation analyses of a cantilever homogeneous beam and two cantilever FGBs with linearly varying and parabolic lower surfaces, respectively, and the effects of geometric size and material gradient on mechanical behaviour of FGB are investigated further. Comparison with finite element results validates the convergence and accuracy of the proposed non-local model.