Abstract
A mixed layer-wise (LW) higher-order shear deformation theory (HSDT) is developed for the thermal buckling analysis of simply-supported, functionally graded (FG) beams subjected to a uniform temperature change. The material properties of the FG beam are assumed to be dependent on the thickness and temperature variables, and the effective material properties are estimated using either the rule of mixtures or the Mori–Tanaka scheme. The results shown in the numerical examples indicate the mixed LW HSDT solutions for critical temperature change parameters are in excellent agreement with the accurate solutions available in the literature. A multi-objective optimization of FG beams is presented to maximize the critical temperature change parameters and to minimize their total mass using a non-dominated sorting-based genetic algorithm. Some specific forms for the volume fractions of the constituents of the FG beam are assumed in advance, such as the one- and three-parameter power-law functions. The former is used in the thermal buckling analysis of the FG beams for comparison purposes, and the latter is used in their optimal design.
Highlights
Graded (FG) beams, plates, and shells are emerging heterogeneous material structures, which are formed by mixing two- or multiple-phase materials with a pre-designed spatial distribution of volume fractions of the constituents [1,2,3,4]
The authors consider the multi-objective optimization of the volume fractions of the constituents of Functionally graded (FG) beams subjected to a uniform temperature change in order to maximize the critical temperature change parameter of the FG beam and to minimize its total mass
The authors developed a mixed LW higher-order shear deformation theory (HSDT) for the thermal buckling analysis of FG beams subjected to a uniform temperature change, and they further developed a non-dominated sorting-based genetic algorithm (GA) for multi-objectives optimization of the material composition of a three-parameter FG beam, in which the TI and TD material properties are considered
Summary
Graded (FG) beams, plates, and shells are emerging heterogeneous material structures, which are formed by mixing two- or multiple-phase materials with a pre-designed spatial distribution of volume fractions of the constituents [1,2,3,4]. Based on an LW higher-order shear deformation theory (HSDT), Pandey and Pradyumna [39] developed a finite element method (FEM) for the static and dynamic analyses of FG sandwich plates. Wu and Xu [45] extended this approach to develop the strong and weak formulations of a mixed higher-order shear deformation theory for the static analysis of FG beams under thermo-mechanical loads. Some articles related to the optimal design of LC structures and FG beams have been presented using different single-and multi-objective optimization algorithms combined with advanced and refined shear deformation beam theories. Na and Kim [64,65,66] investigated the volume fraction optimization of FG plates and panels under thermal loads to minimize the induced thermal stresses and to maximize the critical temperature parameters, in which a bi-objective optimization was considered and the optimal tool was a quasi-Newton method. The through-thickness distribution of the material properties of the FG beam is assumed to be a three-parameter power-law function of the volume fractions of the constituents [71,72], the material-property gradient indices of which are, to be determined for the optimal material profile
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