Exact solutions for postbuckling of a graded porous beam

2018 International Conference on Material Strength and Applied Mechanics

材料科学;力学

Ma, L.S.^1 ; Ou, Z.Y.^1

School of Science, Lanzhou University of Technology, Lanzhou

730050, China^1

关键词: Classical beam theory;    Closed form solutions;    Integral-differential equations;    Nonlinear equilibrium;    Physical neutral surfaces;    Porosity distributions;    Postbuckling behavior;    Transverse deformation;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/372/1/012027/pdf
DOI  :  10.1088/1757-899X/372/1/012027

来源: IOP

【 摘 要 】

An exact, closed-form solution for the postbuckling responses of graded porous beams subjected to axially loading is obtained. It was assumed that the properties of the graded porous materials vary continuously through thickness of the beams, the equations governing the axial and transverse deformations are derived based on the classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for postbuckled deformation is obtained as a function of the applied load. The exact solutions explicitly describe the nonlinear equilibrium paths of the buckled beam and thus are able to provide insight into deformation problems. Based on the exact solutions obtained herein, the effects of various factors such as porosity distribution pattern, porosity coefficient and boundary conditions on postbuckling behavior of graded porous beams have been investigated.