Optimal weight for buckling of FG beam under variable axial load using Pareto optimality

Abstract

In real situation, magnitude, distribution and/or location of axial loads causing a buckling are not known precisely, due to a lack of loading under different operational conditions. Thus, functionally graded structures have to be designed optimally in order to realize their potential. For this reason, this article investigates buckling of functionally graded (FG) beam under variable axial load and optimizes its wight to get the maximum buckling load. The gradation of beam through the thickness direction is described by different function distributions (i.e.; symmetric power and sigmoidal functions). Equations of equilibrium are developed on the basis of higher order shear deformation beam theory by using Hamilton’s principles. Load distribution through the axial direction is portrayed by step, linear and parabolical continuous functions. Numerical differential quadrature method (DQM) is used to solve the equilibrium equations and get buckling loads. Multiobjective optimization procedure is performed to design FG beams under varying axial load for maximum buckling load and minimum weight objectives. Pareto front representation of the best light weight design of a beam under variable axial load that maximizes the critical buckling load parameter is predicted through optimization process. The proposed model is efficient in analysis, design and optimizing an isotropic and FG beam under variable in-plane load.