Nonlinear Buckling Analysis of Functionally Graded Graphene Reinforced Composite Shallow Arches with Elastic Rotational Constraints under Uniform Radial Load

Abstract

The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL’s dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.

Application of the Finite Element Method in the Analysis of Composite Materials: A Review

“…These analyses help determine the best geometry and material for each part of the aircraft, and understand how it will behave in service; for example, how the pressure and drag force will affect the aircraft during a flight [285,287]. Huang [277] and Yang [278] still commented on the introduction of nanostructured materials in aircraft, which will help to increase the resistance and decrease their structural weight. These composites taken with the multifunctional ones have been the subjects of several studies in the last decade, as they present significant improvements in mechanical, chemical, electrical and thermal properties; in other words, not only mechanical support functions, but also integrated functions [278][279][280][281][282][283].…”

“…For designers, the advance of FEM in composites has helped to elaborate hybrid constructions, wherein fiber-reinforced polymeric composites are used as reinforcements, for example, of bridges and columns, besides helping analyze the effects of natural events such as earthquakes, tornados and hurricanes on builds [142,[318][319][320][321]. In addition, as in the aerospace sector, the new nanostructured composites have been helping to reduce the structural weights of the constructions [277,322]. In addition, Oliveira [311] cited a major innovation of the WEG company, which "wanted to replace the steel cover that contains the rotor coil head with an alternative material in a new line of turbogenerators.…”

Analytical Prediction for Nonlinear Buckling of Elastically Supported FG-GPLRC Arches under a Central Point Load

“…Yang and his co-workers conducted pioneering studies on the mechanical behaviors of FG-GPLRC structures, such as beams [25][26][27][28], shells [29,30], and plates [31,32]. Focusing on the stability analysis of FG-GPLRC arches, the authors devoted extensive efforts to the investigation of such structures, including the characteristics of nonlinear static buckling, dynamic buckling, and free vibration for FG-GPLRC arches with different boundary conditions and external loads [33][34][35][36][37][38][39]. In addition, Liu et al [40] analyzed the nonlinear behavior and stability of functionally graded porous (FGP) arches reinforced by GPLs and obtained the critical buckling load under a uniform load.…”

Mechanical buckling analysis of functionally graded composite laminated plates reinforced with temperature dependent graphene sheets resting on elastic foundation

“…Huang et al [9] studied the nonlinear buckling treatment of the GPL reinforced composite shallow arches subjected to a uniform radial load. The equations of motion were derived using the virtual work principle.…”