Robust topology optimization of graphene platelets reinforced functionally graded materials considering hybrid bounded uncertainties

An efficient scheme for the robust topology optimization considering hybrid bounded uncertainties (RTOHBU) is proposed for the graphene platelets (GPLs) reinforced functionally graded materials (FGMs). By introducing the concept of the layer-wise FGMs, the properties of the GPLs reinforced FGMs are calculated based on the Halpin-Tsai micromechanics model. The practical boundedness of probabilistic variables is naturally ensured by utilizing a generalized Beta distribution in constructing the robust topology optimization model. To address the issue of lacking the information of critical loads in existing topology optimization approaches considering hybrid uncertainties, a gradient-attributed search is carried out at first based on the hypothesis of linear elasticity to determine the critical loads leading to the worst structural performance. Subsequently, the statistical characteristics of the objective structural performance under such critical loads are efficiently evaluated by integrating the univariate dimension reduction method and the Gauss-Laguerre quadrature, the accuracy of which is verified by the comparison analysis utilizing the results of Monte Carlo simulation as references. Furthermore, a novel realization vector set is constructed for the bounded probabilistic uncertainties to parallelize the sensitivity analysis and accelerate the optimization process. All the proposed innovations are integrated into the robust topology optimization scheme, the effectiveness and efficiency of which are verified by three illustrative examples.

Vibration characteristics of rotating functionally graded porous beams reinforced by graphene platelets

This work aims to study the vibration characteristics of the rotating functionally graded porous beam reinforced by graphene platelets. The beam is mounted and rotated around a hub with a constant velocity. The material properties vary along the thickness direction with two types of porosity distributions and two dispersion patterns of graphene platelet. The equations of motion based on the Timoshenko beam theory are obtained and solved using the Chebyshev-Ritz method. The effects of the parameters such as hub radius, rotating speed, weight fraction, porosity distribution, porosity coefficient, and dispersion model are presented. The present method results are also compared with numerical results available in the literature.

Multi-layer polymer beam reinforced by graphene platelets on low velocity impact response

Purpose The purpose of this paper is to investigate the effect of graphene platelets (GPLs) on the low-speed contact between a mass and surface of a multi-layer polymer beam. Design/methodology/approach This problem is primarily organized by first-order shear deformation beam theory and nonlinear Hertz rule. GPLs are distributed along the beam thickness direction. The Halpin–Tsai micromechanics model is applied for computing the effective Young’s modulus of the GPLs/polymer composites. In the formulation process, the principle of conservation of energy is first used and the histories of results are extracted using the separation of variables and Runge–Kutta method. Findings In comparing the responses with the available data, a good agreement is observed. The effects of the weight fraction and distribution pattern on the impact response of polymer beam reinforced with GPLs are studied. Results show that contact force is increased, contact time and beam recess are decreased with increasing of weight fraction of GPLs. Also, among the different distribution patterns, the contact force depended on value of GPLs at the point of contact. Originality/value The effects of GPLs addition on the multi-layer polymer beam has a novelty in impact problems.

Laboratory Evaluation of Mechanical Properties of Modified Asphalt and Mixture Using Graphene Platelets (GnPs)

Recently, nanomaterials have attracted attention in the field of pavement construction as modifiers to endure heavy loads and climate changes. In this study, conventional asphalt (bitumen) of penetration grade AC (60/70) was modified with graphene platelets (GnPs) at three different contents: 0.5%, 1.0%, and 1.5% by weight of asphalt content. Kinematic viscosity, softening point, penetration, and dynamic shear rheology tests were performed to evaluate the mechanical properties of modified binder. The results showed that adding GnPs improves the mechanical properties of asphalt binder; the kinematic viscosities, softening points, and rutting parameters increased but penetrations decreased with the contents of GnPs. Hot mix asphalt specimens with GnPs-modified asphalt were prepared and characterized with Marshall tests, thermal stress restrained specimen tests (TSRST), wheel tracking tests, and indirect tensile tests. Similar to the results of asphalt binder, the mechanical properties of asphalt mixture were improved by GnPs. Marshall stability increased by 21% and flow decreased by 24% with accepted value of 2.8 mm in penetration when the mixture was modified with 1.0 wt% of GnPs. At the same GnPs content, modified asphalt mixture led to lower failure temperature by 2 °C in comparison with unmodified asphalt mixture and the cryogenic failure stress was improved by 12%. The wheel tracking tests showed that GnPs-modified asphalt mixture has outstanding deformation resistance in comparison with unmodified asphalt mixtures: after 5000 cycles, 1.0 wt% of GnPs reduced the rut depth of asphalt mixture by 60%—the rut depth of unmodified asphalt mixture was 6.9 mm compared to 2.75 mm for modified asphalt mixture. After 10,000 cycles, the modified asphalt mixture showed rut depth of 3.24 mm in comparison with 8.12 mm in case of unmodified asphalt mixture. Addition of GnPs into asphalt mixture significantly improved the indirect tensile strength: 1.0 wt% of GnPs increased the indirect tensile strength of unmodified asphalt mixture from 0.79 to 1.1 MPa recording ~40% increment. The results of this study can confirm that graphene platelets enhance the mechanical properties of asphalt mixture and its performance.